Herleid\left(-2\sqrt6\right)^2\left(-2\sqrt6\right)\left(\right)-2\sqrt6\left(\right)-2\sqrt{\placeholder{}}\left(\right)-2\left(\right)-\left(\right?
Rekenen met wortels deel 3
In deze samenvatting leer je hoe je kunt herleiden met wortels en hoe je een wortel uit de noemer kunt wegwerken. Laten we beginnen met de rekenregels voor wortels.
Rekenregels voor wortels
De regels die je al eerder hebt geleerd voor wortels zijn:
\left(\sqrt{a}\right)^2=a\left(\sqrt{a}\right)^2=\left(\sqrt{a}\right)^2\left(\sqrt{a}\right)\left(\right)\sqrt{a}\left(\right)\sqrt{a)}\left(\right)\sqrt{a}\left(\right)\sqrt{\placeholder{}}\left(\right?\left(\right.\left(\right)\left(\right)\sqrt{}\left(\right)\sqrt{a}\left(\right)\sqrt{a)}\left(\right)\sqrt{a)}=\left(\right)\sqrt{a)}=A\sqrt{a)}=A\sqrt{a}=A\sqrt{a^{}}=A\sqrt{a^2}=A\sqrt{^2}=A\sqrt{A^2}=A\sqrt{A^2}=\sqrt{^2}=\sqrt{a^2}=\sqrt{a^2}\sqrt{a}\sqrt{\placeholder{}}
\sqrt{a}\cdot\sqrt{b}=\sqrt{ab}\sqrt{a}\cdot\sqrt{b}=\sqrt{a}\sqrt{a}\cdot\sqrt{b}=\sqrt{\placeholder{}}\sqrt{a}\cdot\sqrt{b}=\sqrt{a}\cdot\sqrt{b}\sqrt{a}\cdot\sqrt{\placeholder{}}\sqrt{a}\cdot\sqrt{a}\sqrt{\placeholder{}}
\frac{\sqrt{a}}{\sqrt{b}}=\sqrt{\frac{a}{b}}\frac{\sqrt{a}}{\sqrt{b}}=\sqrt{\frac{a}{\placeholder{}}}\frac{\sqrt{a}}{\sqrt{b}}=\sqrt{\frac{\placeholder{}}{\placeholder{}}}\frac{\sqrt{a}}{\sqrt{b}}=\sqrt{\placeholder{}}\frac{\sqrt{a}}{\sqrt{b}}=\frac{\sqrt{a}}{\sqrt{b}}\frac{\sqrt{a}}{\sqrt{\placeholder{}}}\frac{\sqrt{a}}{\placeholder{}}\frac{\sqrt{\placeholder{}}}{\placeholder{}}\frac{\placeholder{}}{\placeholder{}}
Voorbeelden
Voorbeeld 1: Herleid \left(-4\sqrt3\right)^2 \left(-4\sqrt3\right)^2\left(-4\sqrt3\right)\left(\right)-4\sqrt3\left(\right)-4\sqrt{3)}\left(\right)-4\sqrt3\left(\right)-4\sqrt{\placeholder{}}\left(\right)-4\left(\right)-\left(\right?
Neem over wat je moet herleiden:. Dit betekent:
(-4)^2\cdot(\sqrt3)^2=16\cdot3=48(-4)^2\cdot(\sqrt3)^2=16\cdot3=48(-4)^2\cdot(\sqrt3)^2=16\cdot3=48(-4)^2\cdot(\sqrt3)^2=163=48(-4)^2\cdot(\sqrt3)^2=163=48(-4)^2\cdot(\sqrt3)^2=163=48(-4)^2\cdot(\sqrt3)^2=163=48(-4)^2\cdot(\sqrt3)^2=163=48(-4)^2\cdot(\sqrt3)^2=163=48(-4)^2\cdot(\sqrt3)^2=16\times3=48(-4)^2(\sqrt3)^2=16\times3=48(-4)^2(\sqrt3)^2=16\times3=48(-4)^2(\sqrt3)^2=16\times3=48(-4)^2(\sqrt3)^2=16\times3=48(-4)^2(\sqrt3)^2=16\times3=48(-4)^2(\sqrt3)^2=16\times3=48(-4)^2\times(\sqrt3)^2=16\times3=48(-4)^2\times()^2=16\times3=48(-4)^2\times()^2=16\times3=48(-4)^2\times()^2=16\times3=48(-4)^2\times()^2=16\times3=48(-4)^2\times()^2=16\times3=48(-4)^2\times()^2=16\times3=48(-4)^2\times()^2=16\times3=48(-4)^2\times()^2=16\times3=48(-4)^2\times()^2=16\times3=48(-4)^2\times(3)^2=16\times3=48(-4)^2\times(\surd3)^2=16\times3=48(-4)^2\times(\surd3)=16\times3=48(-4)^2\times(\surd3)^=16\times3=48(-4)^2\times(\surd3)^{2}=16\times3=48(-4)\times(\surd3)^{2}=16\times3=48(-4)^\times(\surd3)^{2}=16\times3=48(-4)² × (√3)² = 16 × 3 = 48(-4)² × (√3)² = 16 × 3 = 48
Voorbeeld 2: Herleid\sqrt5\cdot\sqrt{11}\sqrt5\cdot\sqrt1\sqrt5\cdot\sqrt{\placeholder{}}\sqrt5\cdot\sqrt5\sqrt{\placeholder{}}
Je mag de wortels samenvoegen:
\sqrt{5\cdot11}=\sqrt{55}\sqrt{5\cdot11}=\sqrt{55}\sqrt{5\cdot1}=\sqrt{55}\sqrt{5\cdot}=\sqrt{55}\sqrt5=\sqrt{55}\sqrt5=\sqrt{55}\sqrt5=\sqrt{55}\sqrt5=\sqrt{55}\sqrt5=\sqrt{55}\sqrt5=\sqrt{55}\sqrt{}=\sqrt{55}\sqrt{(}=\sqrt{55}\sqrt{(}5=\sqrt{55}\sqrt{(}5\times=\sqrt{55}\sqrt{(}5\times1=\sqrt{55}\sqrt{(}5\times11=\sqrt{55}\sqrt{(}5\times11)=\sqrt{55}5\times11)=\sqrt{55}5\times11)=\sqrt{55}5\times11)=\sqrt{55}5\times11)=\sqrt{55}5\times11)=\sqrt{55}5\times11)=\sqrt{55}5\times11)=\sqrt{55}\surd5\times11)=\sqrt{55}\surd(5\times11)=\sqrt{55}\surd(5\times11)=\surd(5\times11)=\surd(5\times11)=\surd(5\times11)=\surd(5\times11)=\surd(5\times11)=\surd(5\times11)=\surd(5\times11)=\surd(5\times11)=\surd(5\times11)=\surd(5\times11)=\surd\surd(5\times11)=\surd5√(5 × 11) = √55√(5 × 11) = √55
Voorbeeld 3: Herleid5\sqrt2\cdot3\sqrt{50}5\sqrt2\cdot3\sqrt55\sqrt2\cdot3\sqrt{\placeholder{}}5\sqrt2\cdot35\sqrt2\cdot5\sqrt25\sqrt{\placeholder{}}5
Bij vermenigvuldiging mag je de factoren wisselen:
(5\cdot3)\cdot(\sqrt2\cdot\sqrt{50})=15\cdot\sqrt{100}=15\cdot10=150(5\cdot3)\cdot(\sqrt2\cdot\sqrt{50})=15\cdot\sqrt{100}=1510=150(5\cdot3)\cdot(\sqrt2\cdot\sqrt{50})=15\cdot\sqrt{100}=1510=150(5\cdot3)\cdot(\sqrt2\cdot\sqrt{50})=15\cdot\sqrt{100}=1510=150(5\cdot3)\cdot(\sqrt2\cdot\sqrt{50})=15\cdot\sqrt{100}=1510=150(5\cdot3)\cdot(\sqrt2\cdot\sqrt{50})=15\cdot\sqrt{100}=1510=150(5\cdot3)\cdot(\sqrt2\cdot\sqrt{50})=15\cdot\sqrt{100}=1510=150(5\cdot3)\cdot(\sqrt2\cdot\sqrt{50})=15\cdot\sqrt{100}=15\times10=150(5\cdot3)\cdot(\sqrt2\cdot\sqrt{50})=15\cdot=15\times10=150(5\cdot3)\cdot(\sqrt2\cdot\sqrt{50})=15\cdot=15\times10=150(5\cdot3)\cdot(\sqrt2\cdot\sqrt{50})=15\cdot=15\times10=150(5\cdot3)\cdot(\sqrt2\cdot\sqrt{50})=15\cdot=15\times10=150(5\cdot3)\cdot(\sqrt2\cdot\sqrt{50})=15\cdot=15\times10=150(5\cdot3)\cdot(\sqrt2\cdot\sqrt{50})=15\cdot=15\times10=150(5\cdot3)\cdot(\sqrt2\cdot\sqrt{50})=15\cdot=15\times10=150(5\cdot3)\cdot(\sqrt2\cdot\sqrt{50})=15\cdot=15\times10=150(5\cdot3)\cdot(\sqrt2\cdot\sqrt{50})=15\cdot=15\times10=150(5\cdot3)\cdot(\sqrt2\cdot\sqrt{50})=15\cdot=15\times10=150(5\cdot3)\cdot(\sqrt2\cdot\sqrt{50})=15\cdot=15\times10=150(5\cdot3)\cdot(\sqrt2\cdot\sqrt{50})=15\cdot=15\times10=150(5\cdot3)\cdot(\sqrt2\cdot\sqrt{50})=15\cdot=15\times10=150(5\cdot3)\cdot(\sqrt2\cdot\sqrt{50})=15\cdot(=15\times10=150(5\cdot3)\cdot(\sqrt2\cdot\sqrt{50})=15\cdot(\surd=15\times10=150(5\cdot3)\cdot(\sqrt2\cdot\sqrt{50})=15\cdot(\surd)=15\times10=150(5\cdot3)\cdot(\sqrt2\cdot\sqrt{50})=15\cdot(\surd1)=15\times10=150(5\cdot3)\cdot(\sqrt2\cdot\sqrt{50})=15\cdot(\surd10)=15\times10=150(5\cdot3)\cdot(\sqrt2\cdot\sqrt{50})=15\cdot(\surd100)=15\times10=150(5\cdot3)\cdot(\sqrt2\cdot\sqrt{50})=15(\surd100)=15\times10=150(5\cdot3)\cdot(\sqrt2\cdot\sqrt{50})=15(\surd100)=15\times10=150(5\cdot3)\cdot(\sqrt2\cdot\sqrt{50})=15(\surd100)=15\times10=150(5\cdot3)\cdot(\sqrt2\cdot\sqrt{50})=15(\surd100)=15\times10=150(5\cdot3)\cdot(\sqrt2\cdot\sqrt{50})=15(\surd100)=15\times10=150(5\cdot3)\cdot(\sqrt2\cdot\sqrt{50})=15(\surd100)=15\times10=150(5\cdot3)\cdot(\sqrt2\cdot\sqrt{50})=15\times(\surd100)=15\times10=150(5\cdot3)\cdot(\sqrt2\cdot)=15\times(\surd100)=15\times10=150(5\cdot3)\cdot(\sqrt2\cdot)=15\times(\surd100)=15\times10=150(5\cdot3)\cdot(\sqrt2\cdot)=15\times(\surd100)=15\times10=150(5\cdot3)\cdot(\sqrt2\cdot)=15\times(\surd100)=15\times10=150(5\cdot3)\cdot(\sqrt2\cdot)=15\times(\surd100)=15\times10=150(5\cdot3)\cdot(\sqrt2\cdot)=15\times(\surd100)=15\times10=150(5\cdot3)\cdot(\sqrt2\cdot)=15\times(\surd100)=15\times10=150(5\cdot3)\cdot(\sqrt2\cdot)=15\times(\surd100)=15\times10=150(5\cdot3)\cdot(\sqrt2\cdot)=15\times(\surd100)=15\times10=150(5\cdot3)\cdot(\sqrt2\cdot)=15\times(\surd100)=15\times10=150(5\cdot3)\cdot(\sqrt2\cdot\surd)=15\times(\surd100)=15\times10=150(5\cdot3)\cdot(\sqrt2\cdot\surd5)=15\times(\surd100)=15\times10=150(5\cdot3)\cdot(\sqrt2\cdot\surd50)=15\times(\surd100)=15\times10=150(5\cdot3)\cdot(\sqrt2\surd50)=15\times(\surd100)=15\times10=150(5\cdot3)\cdot(\sqrt2\surd50)=15\times(\surd100)=15\times10=150(5\cdot3)\cdot(\sqrt2\surd50)=15\times(\surd100)=15\times10=150(5\cdot3)\cdot(\sqrt2\surd50)=15\times(\surd100)=15\times10=150(5\cdot3)\cdot(\sqrt2\surd50)=15\times(\surd100)=15\times10=150(5\cdot3)\cdot(\sqrt2\surd50)=15\times(\surd100)=15\times10=150(5\cdot3)\cdot(\sqrt2\times\surd50)=15\times(\surd100)=15\times10=150(5\cdot3)\cdot(\times\surd50)=15\times(\surd100)=15\times10=150(5\cdot3)\cdot(\times\surd50)=15\times(\surd100)=15\times10=150(5\cdot3)\cdot(\times\surd50)=15\times(\surd100)=15\times10=150(5\cdot3)\cdot(\times\surd50)=15\times(\surd100)=15\times10=150(5\cdot3)\cdot(\times\surd50)=15\times(\surd100)=15\times10=150(5\cdot3)\cdot(\times\surd50)=15\times(\surd100)=15\times10=150(5\cdot3)\cdot(\times\surd50)=15\times(\surd100)=15\times10=150(5\cdot3)\cdot(\times\surd50)=15\times(\surd100)=15\times10=150(5\cdot3)\cdot(\times\surd50)=15\times(\surd100)=15\times10=150(5\cdot3)\cdot(\times\surd50)=15\times(\surd100)=15\times10=150(5\cdot3)\cdot(\times\surd50)=15\times(\surd100)=15\times10=150(5\cdot3)\cdot(\surd\times\surd50)=15\times(\surd100)=15\times10=150(5\cdot3)\cdot(\surd2\times\surd50)=15\times(\surd100)=15\times10=150(5\cdot3)(\surd2\times\surd50)=15\times(\surd100)=15\times10=150(5\cdot3)(\surd2\times\surd50)=15\times(\surd100)=15\times10=150(5\cdot3)(\surd2\times\surd50)=15\times(\surd100)=15\times10=150(5\cdot3)(\surd2\times\surd50)=15\times(\surd100)=15\times10=150(5\cdot3)(\surd2\times\surd50)=15\times(\surd100)=15\times10=150(5\cdot3)(\surd2\times\surd50)=15\times(\surd100)=15\times10=150(5\cdot3)\times(\surd2\times\surd50)=15\times(\surd100)=15\times10=150(53)\times(\surd2\times\surd50)=15\times(\surd100)=15\times10=150(53)\times(\surd2\times\surd50)=15\times(\surd100)=15\times10=150(53)\times(\surd2\times\surd50)=15\times(\surd100)=15\times10=150(53)\times(\surd2\times\surd50)=15\times(\surd100)=15\times10=150(53)\times(\surd2\times\surd50)=15\times(\surd100)=15\times10=150(53)\times(\surd2\times\surd50)=15\times(\surd100)=15\times10=150(5\cdoy3)\times(\surd2\times\surd50)=15\times(\surd100)=15\times10=150(53)\times(\surd2\times\surd50)=15\times(\surd100)=15\times10=150(53)\times(\surd2\times\surd50)=15\times(\surd100)=15\times10=150(53)\times(\surd2\times\surd50)=15\times(\surd100)=15\times10=150(53)\times(\surd2\times\surd50)=15\times(\surd100)=15\times10=150(53)\times(\surd2\times\surd50)=15\times(\surd100)=15\times10=150(53)\times(\surd2\times\surd50)=15\times(\surd100)=15\times10=150(5 × 3) × (√2 × √50) = 15 × (√100) = 15 × 10 = 150(5 × 3) × (√2 × √50) = 15 × (√100) = 15 × 10 = 150
Voorbeeld 4: Herleid\frac{\sqrt{24}}{\sqrt8}\frac{\sqrt{24}}{\sqrt{\placeholder{}}}\frac{\sqrt{24}}{\placeholder{}}\frac{\sqrt2}{\placeholder{}}\frac{\sqrt{\placeholder{}}}{\placeholder{}}\frac{\placeholder{}}{\placeholder{}}
Je mag de wortels samenvoegen:
\sqrt{\frac{24}{8}}=\sqrt3\sqrt{\frac{24}{8}}=\sqrt{\frac{24}{8}}=\sqrt{\frac{24}{8}}=\sqrt{\frac{24}{8}}=\sqrt{\frac{24}{8}}=\sqrt{\frac{24}{8}}=\sqrt{\frac{24}{8}}=\sqrt{\frac{24}{8}}=\sqrt{\frac{24}{8}}=\sqrt{\frac{24}{8}}=\surd\sqrt{\frac{24}{8}}=\surd3\sqrt{\frac{24}{8}}\frac{}{8}=\surd3\sqrt{\frac{24}{8}}\frac28=\surd3\sqrt{\frac{24}{8}}\frac{24}{8}=\surd3\sqrt{\frac{24}{\placeholder{}}}\frac{24}{8}=\surd3\sqrt{\frac{2}{\placeholder{}}}\frac{24}{8}=\surd3\sqrt{\frac{\placeholder{}}{\placeholder{}}}\frac{24}{8}=\surd3\sqrt{\placeholder{}}\frac{24}{8}=\surd3\frac{24}{8}=\surd3\surd\frac{24}{8}=\surd3\surd\frac{24}{8})=\surd3\surd(\frac{24}{8})=\surd3\surd(\frac{24}{8}8)=\surd3\surd(\frac{24}{\placeholder{}}8)=\surd3\surd(248)=\surd3√(24 / 8) = √3√(24 / 8) = √3
Voorbeeld 5: Herleid\frac{6\sqrt{80}}{2\sqrt5}\frac{6\sqrt{80}}{2\sqrt{\placeholder{}}}\frac{6\sqrt{80}}{2}\frac{6\sqrt{80}}{\placeholder{}}\frac{6\sqrt8}{\placeholder{}}\frac{6\sqrt{\placeholder{}}}{\placeholder{}}\frac{6}{\placeholder{}}\frac{\placeholder{}}{\placeholder{}}
Je mag delen en de wortels samenvoegen:
\frac{6\sqrt{80}}{2\sqrt5}=3\cdot\sqrt{\frac{80}{5}}=3\cdot\sqrt{16}=3\cdot4=12\frac{6\sqrt{80}}{2\sqrt5}=3\cdot\sqrt{\frac{80}{5}}=3\cdot\sqrt{16}=34=12\frac{6\sqrt{80}}{2\sqrt5}=3\cdot\sqrt{\frac{80}{5}}=3\cdot\sqrt{16}=34=12\frac{6\sqrt{80}}{2\sqrt5}=3\cdot\sqrt{\frac{80}{5}}=3\cdot\sqrt{16}=34=12\frac{6\sqrt{80}}{2\sqrt5}=3\cdot\sqrt{\frac{80}{5}}=3\cdot\sqrt{16}=34=12\frac{6\sqrt{80}}{2\sqrt5}=3\cdot\sqrt{\frac{80}{5}}=3\cdot\sqrt{16}=34=12\frac{6\sqrt{80}}{2\sqrt5}=3\cdot\sqrt{\frac{80}{5}}=3\cdot\sqrt{16}=34=12\frac{6\sqrt{80}}{2\sqrt5}=3\cdot\sqrt{\frac{80}{5}}=3\cdot\sqrt{16}=3\times4=12\frac{6\sqrt{80}}{2\sqrt5}=3\cdot\sqrt{\frac{80}{5}}=3\sqrt{16}=3\times4=12\frac{6\sqrt{80}}{2\sqrt5}=3\cdot\sqrt{\frac{80}{5}}=3\sqrt{16}=3\times4=12\frac{6\sqrt{80}}{2\sqrt5}=3\cdot\sqrt{\frac{80}{5}}=3\sqrt{16}=3\times4=12\frac{6\sqrt{80}}{2\sqrt5}=3\cdot\sqrt{\frac{80}{5}}=3\sqrt{16}=3\times4=12\frac{6\sqrt{80}}{2\sqrt5}=3\cdot\sqrt{\frac{80}{5}}=3\sqrt{16}=3\times4=12\frac{6\sqrt{80}}{2\sqrt5}=3\cdot\sqrt{\frac{80}{5}}=3\sqrt{16}=3\times4=12\frac{6\sqrt{80}}{2\sqrt5}=3\cdot\sqrt{\frac{80}{5}}=3\times\sqrt{16}=3\times4=12\frac{6\sqrt{80}}{2\sqrt5}=3\sqrt{\frac{80}{5}}=3\times\sqrt{16}=3\times4=12\frac{6\sqrt{80}}{2\sqrt5}=3\sqrt{\frac{80}{5}}=3\times\sqrt{16}=3\times4=12\frac{6\sqrt{80}}{2\sqrt5}=3\sqrt{\frac{80}{5}}=3\times\sqrt{16}=3\times4=12\frac{6\sqrt{80}}{2\sqrt5}=3\sqrt{\frac{80}{5}}=3\times\sqrt{16}=3\times4=12\frac{6\sqrt{80}}{2\sqrt5}=3\sqrt{\frac{80}{5}}=3\times\sqrt{16}=3\times4=12\frac{6\sqrt{80}}{2\sqrt5}=3\sqrt{\frac{80}{5}}=3\times\sqrt{16}=3\times4=12\frac{6\sqrt{80}}{2\sqrt5}=3\times\sqrt{\frac{80}{5}}=3\times\sqrt{16}=3\times4=12\frac{6\sqrt{80}}{2\sqrt5}=3\times\sqrt{\frac{80}{5}}=3\times=3\times4=12\frac{6\sqrt{80}}{2\sqrt5}=3\times\sqrt{\frac{80}{5}}=3\times=3\times4=12\frac{6\sqrt{80}}{2\sqrt5}=3\times\sqrt{\frac{80}{5}}=3\times=3\times4=12\frac{6\sqrt{80}}{2\sqrt5}=3\times\sqrt{\frac{80}{5}}=3\times=3\times4=12\frac{6\sqrt{80}}{2\sqrt5}=3\times\sqrt{\frac{80}{5}}=3\times=3\times4=12\frac{6\sqrt{80}}{2\sqrt5}=3\times\sqrt{\frac{80}{5}}=3\times=3\times4=12\frac{6\sqrt{80}}{2\sqrt5}=3\times\sqrt{\frac{80}{5}}=3\times=3\times4=12\frac{6\sqrt{80}}{2\sqrt5}=3\times\sqrt{\frac{80}{5}}=3\times=3\times4=12\frac{6\sqrt{80}}{2\sqrt5}=3\times\sqrt{\frac{80}{5}}=3\times=3\times4=12\frac{6\sqrt{80}}{2\sqrt5}=3\times\sqrt{\frac{80}{5}}=3\times=3\times4=12\frac{6\sqrt{80}}{2\sqrt5}=3\times\sqrt{\frac{80}{5}}=3\times=3\times4=12\frac{6\sqrt{80}}{2\sqrt5}=3\times\sqrt{\frac{80}{5}}=3\times=3\times4=12\frac{6\sqrt{80}}{2\sqrt5}=3\times\sqrt{\frac{80}{5}}=3\times\surd=3\times4=12\frac{6\sqrt{80}}{2\sqrt5}=3\times\sqrt{\frac{80}{5}}=3\times\surd1=3\times4=12\frac{6\sqrt{80}}{2\sqrt5}=3\times\sqrt{\frac{80}{5}}=3\times\surd16=3\times4=12\frac{6\sqrt{80}}{2\sqrt5}=3\times\surd\sqrt{\frac{80}{5}}=3\times\surd16=3\times4=12\frac{6\sqrt{80}}{2\sqrt5}=3\times\surd(\sqrt{\frac{80}{5}}=3\times\surd16=3\times4=12\frac{6\sqrt{80}}{2\sqrt5}=3\times\surd(8\sqrt{\frac{80}{5}}=3\times\surd16=3\times4=12\frac{6\sqrt{80}}{2\sqrt5}=3\times\surd(80\sqrt{\frac{80}{5}}=3\times\surd16=3\times4=12\frac{6\sqrt{80}}{2\sqrt5}=3\times\surd(80/\sqrt{\frac{80}{5}}=3\times\surd16=3\times4=12\frac{6\sqrt{80}}{2\sqrt5}=3\times\surd(80/5\sqrt{\frac{80}{5}}=3\times\surd16=3\times4=12\frac{6\sqrt{80}}{2\sqrt5}=3\times\surd(80/5)\sqrt{\frac{80}{5}}=3\times\surd16=3\times4=12\frac{6\sqrt{80}}{2\sqrt5}=3\times\surd(80/5)=3\times\surd16=3\times4=12\frac{6\sqrt{80}}{2\sqrt5}=3\times\surd(80/5)=3\times\surd16=3\times4=12\frac{6\sqrt{80}}{2\sqrt5}=3\times\surd(80/5)=3\times\surd16=3\times4=12\frac{6\sqrt{80}}{2\sqrt5}=3\times\surd(80/5)=3\times\surd16=3\times4=12\frac{6\sqrt{80}}{2\sqrt5}=3\times\surd(80/5)=3\times\surd16=3\times4=12\frac{6\sqrt{80}}{2\sqrt5}=3\times\surd(80/5)=3\times\surd16=3\times4=12\frac{6\sqrt{80}}{2\sqrt5}=3\times\surd(80/5)=3\times\surd16=3\times4=12\frac{6\sqrt{80}}{2\sqrt5}=3\times\surd(80/5)=3\times\surd16=3\times4=12\frac{6\sqrt{80}}{2\sqrt5}=3\times\surd(80/5)=3\times\surd16=3\times4=12\frac{6\sqrt{80}}{2\sqrt5}=3\times\surd(80/5)=3\times\surd16=3\times4=12\frac{6\sqrt{80}}{2\sqrt5}=3\times\surd(80/5)=3\times\surd16=3\times4=12\frac{6\sqrt{80}}{2\sqrt5}=3\times\surd(80/5)=3\times\surd16=3\times4=12\frac{6\sqrt{80}}{2\sqrt5}=3\times\surd(80/5)=3\times\surd16=3\times4=12\frac{6\sqrt{80}}{2\sqrt5}=3\times\surd(80/5)=3\times\surd16=3\times4=12\frac{6\sqrt{80}}{2\sqrt5}=3\times\surd(80/5)=3\times\surd16=3\times4=12\frac{6\sqrt{80}}{2\sqrt5}=3\times\surd(80/5)=3\times\surd16=3\times4=12\frac{6\sqrt{80}}{2\sqrt5}=3\times\surd(80/5)=3\times\surd16=3\times4=12\frac{6\sqrt{80}}{2\sqrt5}=3\times\surd(80/5)=3\times\surd16=3\times4=12\frac{6\sqrt{80}}{2\sqrt5}=3\times\surd(80/5)=3\times\surd16=3\times4=12\frac{6\sqrt{80}}{2\sqrt5}=3\times\surd(80/5)=3\times\surd16=3\times4=12\frac{6\sqrt{80}}{2\sqrt5}=3\times\surd(80/5)=3\times\surd16=3\times4=12=3\times\surd(80/5)=3\times\surd16=3\times4=12(6 / 2) × (√80 / √5) = 3 × √(80 / 5) = 3 × √16 = 3 × 4 = 12(6 / 2) × (√80 / √5) = 3 × √(80 / 5) = 3 × √16 = 3 × 4 = 12
Voorbeeld 6: Herleid 2\sqrt3+5\sqrt32\sqrt3+5\sqrt{\placeholder{}}2\sqrt3+52\sqrt3+2\sqrt32\sqrt{\placeholder{}}2
Omdat ze gelijksoortig zijn, mag je ze optellen:
\frac{6\sqrt{80}}{2\sqrt5}=3\cdot\sqrt{\frac{80}{5}}=3\cdot\sqrt{16}=3\cdot4=12 2 √3 + 5 √3 = 7 √32\surd+5\surd3=7\surd32+5\surd3=7\surd32+5\surd3=7\surd32+5\surd3=7\surd32+5\surd3=7\surd32+5\surd3=7\surd32+5\surd3=7\surd32+5\surd3=7\surd32+5\surd3=7\surd32+5\surd3=7\surd32\surd+5\surd3=7\surd3 2 √3 + 5 √3 = 7 √3 2 √3 + 5 √3 = 7 √3
Voorbeeld 7: Herleid 5\sqrt2+5\sqrt35\sqrt2+5\sqrt{\placeholder{}}5\sqrt2+55\sqrt2+5\sqrt25\sqrt255\sqrt25\sqrt{\placeholder{}}5
De wortels zijn niet gelijksoortig, dus je kunt ze niet optellen. Schrijf het als: k.n. (kan niet)
Voorbeeld 8: Herleid 2\sqrt{45}+3\sqrt52\sqrt{45}+3\sqrt{\placeholder{}}2\sqrt{45}+32\sqrt{45}+2\sqrt{45}2\sqrt42\sqrt{\placeholder{}}2
Je kunt een factor uit de wortel halen:
2\cdot\sqrt{9\cdot5}+3\sqrt5=2\cdot\left(3\sqrt5\right)+3\sqrt5=6\surd5+3\surd5=9\surd52\cdot\sqrt{9\cdot5}+3\sqrt5=2\cdot3\sqrt5)+3\sqrt5=6\surd5+3\surd5=9\surd52\cdot\sqrt{9\cdot5}+3\sqrt5=2\cdot3\sqrt5+3\sqrt5=6\surd5+3\surd5=9\surd52\cdot\sqrt{9\cdot5}+3\sqrt5=2\cdot3\sqrt5+3=6\surd5+3\surd5=9\surd52\cdot\sqrt{9\cdot5}+3\sqrt5=2\cdot3\sqrt5+3=6\surd5+3\surd5=9\surd52\cdot\sqrt{9\cdot5}+3\sqrt5=2\cdot3\sqrt5+3=6\surd5+3\surd5=9\surd52\cdot\sqrt{9\cdot5}+3\sqrt5=2\cdot3\sqrt5+3=6\surd5+3\surd5=9\surd52\cdot\sqrt{9\cdot5}+3\sqrt5=2\cdot3\sqrt5+3=6\surd5+3\surd5=9\surd52\cdot\sqrt{9\cdot5}+3\sqrt5=2\cdot3\sqrt5+3=6\surd5+3\surd5=9\surd52\cdot\sqrt{9\cdot5}+3\sqrt5=2\cdot3\sqrt5+3=6\surd5+3\surd5=9\surd52\cdot\sqrt{9\cdot5}+3\sqrt5=2\cdot3\sqrt5+3=6\surd5+3\surd5=9\surd52\cdot\sqrt{9\cdot5}+3\sqrt5=2\cdot3\sqrt5+3=6\surd5+3\surd5=9\surd52\cdot\sqrt{9\cdot5}+3\sqrt5=2\cdot3\sqrt5+3\surd=6\surd5+3\surd5=9\surd52\cdot\sqrt{9\cdot5}+3\sqrt5=2\cdot3\sqrt5+3\surd5=6\surd5+3\surd5=9\surd52\cdot\sqrt{9\cdot5}+3\sqrt5=2\cdot3+3\surd5=6\surd5+3\surd5=9\surd52\cdot\sqrt{9\cdot5}+3\sqrt5=2\cdot3+3\surd5=6\surd5+3\surd5=9\surd52\cdot\sqrt{9\cdot5}+3\sqrt5=2\cdot3+3\surd5=6\surd5+3\surd5=9\surd52\cdot\sqrt{9\cdot5}+3\sqrt5=2\cdot3+3\surd5=6\surd5+3\surd5=9\surd52\cdot\sqrt{9\cdot5}+3\sqrt5=2\cdot3+3\surd5=6\surd5+3\surd5=9\surd52\cdot\sqrt{9\cdot5}+3\sqrt5=2\cdot3+3\surd5=6\surd5+3\surd5=9\surd52\cdot\sqrt{9\cdot5}+3\sqrt5=2\cdot3+3\surd5=6\surd5+3\surd5=9\surd52\cdot\sqrt{9\cdot5}+3\sqrt5=2\cdot3+3\surd5=6\surd5+3\surd5=9\surd52\cdot\sqrt{9\cdot5}+3\sqrt5=2\cdot3+3\surd5=6\surd5+3\surd5=9\surd52\cdot\sqrt{9\cdot5}+3\sqrt5=2\cdot+3\surd5=6\surd5+3\surd5=9\surd52\cdot\sqrt{9\cdot5}+3\sqrt5=2\cdot(+3\surd5=6\surd5+3\surd5=9\surd52\cdot\sqrt{9\cdot5}+3\sqrt5=2\cdot(3+3\surd5=6\surd5+3\surd5=9\surd52\cdot\sqrt{9\cdot5}+3\sqrt5=2\cdot(3\surd+3\surd5=6\surd5+3\surd5=9\surd52\cdot\sqrt{9\cdot5}+3\sqrt5=2\cdot(3\surd5+3\surd5=6\surd5+3\surd5=9\surd52\cdot\sqrt{9\cdot5}+3\sqrt5=2\cdot(3\surd5)+3\surd5=6\surd5+3\surd5=9\surd52\cdot\sqrt{9\cdot5}+3\sqrt5=2\cdot(3\surd)+3\surd5=6\surd5+3\surd5=9\surd52\cdot\sqrt{9\cdot5}+3\sqrt5=2\cdot+3\surd5=6\surd5+3\surd5=9\surd52\cdot\sqrt{9\cdot5}+3\sqrt5=2\cdot(+3\surd5=6\surd5+3\surd5=9\surd52\cdot\sqrt{9\cdot5}+3\sqrt5=2\cdot(3+3\surd5=6\surd5+3\surd5=9\surd52\cdot\sqrt{9\cdot5}+3\sqrt5=2\cdot(3)+3\surd5=6\surd5+3\surd5=9\surd52\cdot\sqrt{9\cdot5}+3\sqrt5=2\cdot(3\surd)+3\surd5=6\surd5+3\surd5=9\surd52\cdot\sqrt{9\cdot5}+3\sqrt5=2\cdot(3\surd5)+3\surd5=6\surd5+3\surd5=9\surd52\cdot\sqrt{9\cdot5}+3\sqrt5=2(3\surd5)+3\surd5=6\surd5+3\surd5=9\surd52\cdot\sqrt{9\cdot5}+3\sqrt5=2(3\surd5)+3\surd5=6\surd5+3\surd5=9\surd52\cdot\sqrt{9\cdot5}+3\sqrt5=2(3\surd5)+3\surd5=6\surd5+3\surd5=9\surd52\cdot\sqrt{9\cdot5}+3\sqrt5=2(3\surd5)+3\surd5=6\surd5+3\surd5=9\surd52\cdot\sqrt{9\cdot5}+3\sqrt5=2(3\surd5)+3\surd5=6\surd5+3\surd5=9\surd52\cdot\sqrt{9\cdot5}+3\sqrt5=2(3\surd5)+3\surd5=6\surd5+3\surd5=9\surd52\cdot\sqrt{9\cdot5}+3\sqrt5=2\times(3\surd5)+3\surd5=6\surd5+3\surd5=9\surd52\cdot\sqrt{9\cdot5}+3=2\times(3\surd5)+3\surd5=6\surd5+3\surd5=9\surd52\cdot\sqrt{9\cdot5}+3=2\times(3\surd5)+3\surd5=6\surd5+3\surd5=9\surd52\cdot\sqrt{9\cdot5}+3=2\times(3\surd5)+3\surd5=6\surd5+3\surd5=9\surd52\cdot\sqrt{9\cdot5}+3=2\times(3\surd5)+3\surd5=6\surd5+3\surd5=9\surd52\cdot\sqrt{9\cdot5}+3=2\times(3\surd5)+3\surd5=6\surd5+3\surd5=9\surd52\cdot\sqrt{9\cdot5}+3=2\times(3\surd5)+3\surd5=6\surd5+3\surd5=9\surd52\cdot\sqrt{9\cdot5}+3=2\times(3\surd5)+3\surd5=6\surd5+3\surd5=9\surd52\cdot\sqrt{9\cdot5}+3=2\times(3\surd5)+3\surd5=6\surd5+3\surd5=9\surd52\cdot\sqrt{9\cdot5}+3=2\times(3\surd5)+3\surd5=6\surd5+3\surd5=9\surd52\cdot\sqrt{9\cdot5}+3\surd=2\times(3\surd5)+3\surd5=6\surd5+3\surd5=9\surd52\cdot\sqrt{9\cdot5}+3\surd5=2\times(3\surd5)+3\surd5=6\surd5+3\surd5=9\surd52\sqrt{9\cdot5}+3\surd5=2\times(3\surd5)+3\surd5=6\surd5+3\surd5=9\surd52\sqrt{9\cdot5}+3\surd5=2\times(3\surd5)+3\surd5=6\surd5+3\surd5=9\surd52\sqrt{9\cdot5}+3\surd5=2\times(3\surd5)+3\surd5=6\surd5+3\surd5=9\surd52\sqrt{9\cdot5}+3\surd5=2\times(3\surd5)+3\surd5=6\surd5+3\surd5=9\surd52\sqrt{9\cdot5}+3\surd5=2\times(3\surd5)+3\surd5=6\surd5+3\surd5=9\surd52\sqrt{9\cdot5}+3\surd5=2\times(3\surd5)+3\surd5=6\surd5+3\surd5=9\surd52\times\sqrt{9\cdot5}+3\surd5=2\times(3\surd5)+3\surd5=6\surd5+3\surd5=9\surd52\times\surd\sqrt{9\cdot5}+3\surd5=2\times(3\surd5)+3\surd5=6\surd5+3\surd5=9\surd52\times\surd(\sqrt{9\cdot5}+3\surd5=2\times(3\surd5)+3\surd5=6\surd5+3\surd5=9\surd52\times\surd(9\sqrt{9\cdot5}+3\surd5=2\times(3\surd5)+3\surd5=6\surd5+3\surd5=9\surd52\times\surd(9\times\sqrt{9\cdot5}+3\surd5=2\times(3\surd5)+3\surd5=6\surd5+3\surd5=9\surd52\times\surd(9\times5\sqrt{9\cdot5}+3\surd5=2\times(3\surd5)+3\surd5=6\surd5+3\surd5=9\surd52\times\surd(9\times5)\sqrt{9\cdot5}+3\surd5=2\times(3\surd5)+3\surd5=6\surd5+3\surd5=9\surd52\times\surd(9\times5)+3\surd5=2\times(3\surd5)+3\surd5=6\surd5+3\surd5=9\surd52\times\surd(9\times5)+3\surd5=2\times(3\surd5)+3\surd5=6\surd5+3\surd5=9\surd52\times\surd(9\times5)+3\surd5=2\times(3\surd5)+3\surd5=6\surd5+3\surd5=9\surd52\times\surd(9\times5)+3\surd5=2\times(3\surd5)+3\surd5=6\surd5+3\surd5=9\surd52\times\surd(9\times5)+3\surd5=2\times(3\surd5)+3\surd5=6\surd5+3\surd5=9\surd52\times\surd(9\times5)+3\surd5=2\times(3\surd5)+3\surd5=6\surd5+3\surd5=9\surd52\times\surd(9\times5)+3\surd5=2\times(3\surd5)+3\surd5=6\surd5+3\surd5=9\surd52\times\surd(9\times5)+3\surd5=2\times(3\surd5)+3\surd5=6\surd5+3\surd5=9\surd52\times\surd(9\times5)+3\surd5=2\times(3\surd5)+3\surd5=6\surd5+3\surd5=9\surd52\times\surd(9\times5)+3\surd5=2\times(3\surd5)+3\surd5=6\surd5+3\surd5=9\surd52\times\surd(9\times5)+3\surd5=2\times(3\surd5)+3\surd5=6\surd5+3\surd5=9\surd52\times\surd(9\times5)+3\surd5=2\times(3\surd5)+3\surd5=6\surd5+3\surd5=9\surd52\times\surd(9\times5)+3\surd5=2\times(3\surd5)+3\surd5=6\surd5+3\surd5=9\surd52\times\surd(9\times5)+3\surd5=2\times(3\surd5)+3\surd5=6\surd5+3\surd5=9\surd52 × √(9 × 5) + 3 √5 = 2 × (3 √5) + 3 √5 = 6 √5 + 3 √5 = 9 √52 × √(9 × 5) + 3 √5 = 2 × (3 √5) + 3 √5 = 6 √5 + 3 √5 = 9 √5
De wortel wegwerken uit de noemer
Als je een breuk hebt met een wortel in de noemer, werk je deze weg met een slimme breuk. Bijvoorbeeld:
Voorbeeld 1: Herleid\frac{8}{\sqrt3}\frac{8}{\sqrt{\placeholder{}}}\frac{8}{\placeholder{}}\frac{8\sqrt{}}{\placeholder{}}\frac{8\sqrt3}{\placeholder{}}\frac{8\sqrt{\placeholder{}}}{\placeholder{}}\frac{8}{\placeholder{}}\frac{\placeholder{}}{\placeholder{}}
Je vermenigvuldigt met\frac{\sqrt3}{\sqrt3}\frac{\sqrt3}{\sqrt{\placeholder{}}}\frac{\sqrt3}{\placeholder{}}\sqrt3\sqrt{\placeholder{}}:
\frac{8}{\sqrt3}\cdot\frac{\sqrt3}{\sqrt3}=\frac{8\sqrt3}{3}\frac{8}{\sqrt3}\cdot\frac{\sqrt3}{\sqrt3}=\frac83\frac{8}{\sqrt3}\cdot\frac{\sqrt3}{\sqrt3}=\frac83\frac{8}{\sqrt3}\cdot\frac{\sqrt3}{\sqrt3}=\frac83\frac{8}{\sqrt3}\cdot\frac{\sqrt3}{\sqrt3}=\frac83\frac{8}{\sqrt3}\cdot\frac{\sqrt3}{\sqrt3}=\frac83\frac{8}{\sqrt3}\cdot\frac{\sqrt3}{\sqrt3}=\frac83\frac{8}{\sqrt3}\cdot\frac{\sqrt3}{\sqrt3}=\frac83\frac{8}{\sqrt3}\cdot\frac{\sqrt3}{\sqrt3}=\frac83\frac{8}{\sqrt3}\cdot\frac{\sqrt3}{\sqrt3}=\frac83\frac{8}{\sqrt3}\cdot\frac{\sqrt3}{\sqrt3}=\frac{8\surd}{3}\frac{8}{\sqrt3}\cdot\frac{\sqrt3}{\sqrt3}=\frac{8√3}{3}\frac{8}{\sqrt3}\cdot\frac{\sqrt3}{}=\frac{8√3}{3}\frac{8}{\sqrt3}\cdot\frac{\sqrt3}{}=\frac{8√3}{3}\frac{8}{\sqrt3}\cdot\frac{\sqrt3}{}=\frac{8√3}{3}\frac{8}{\sqrt3}\cdot\frac{\sqrt3}{}=\frac{8√3}{3}\frac{8}{\sqrt3}\cdot\frac{\sqrt3}{}=\frac{8√3}{3}\frac{8}{\sqrt3}\cdot\frac{\sqrt3}{}=\frac{8√3}{3}\frac{8}{\sqrt3}\cdot\frac{\sqrt3}{}=\frac{8√3}{3}\frac{8}{\sqrt3}\cdot\frac{\sqrt3}{}=\frac{8√3}{3}\frac{8}{\sqrt3}\cdot\frac{\sqrt3}{}=\frac{8√3}{3}\frac{8}{\sqrt3}\cdot\frac{\sqrt3}{\surd}=\frac{8√3}{3}\frac{8}{\sqrt3}\cdot\frac{\sqrt3}{\surd3}=\frac{8√3}{3}\frac{8}{\sqrt3}\cdot\frac{}{\surd3}=\frac{8√3}{3}\frac{8}{\sqrt3}\cdot\frac{}{\surd3}=\frac{8√3}{3}\frac{8}{\sqrt3}\cdot\frac{}{\surd3}=\frac{8√3}{3}\frac{8}{\sqrt3}\cdot\frac{}{\surd3}=\frac{8√3}{3}\frac{8}{\sqrt3}\cdot\frac{}{\surd3}=\frac{8√3}{3}\frac{8}{\sqrt3}\cdot\frac{}{\surd3}=\frac{8√3}{3}\frac{8}{\sqrt3}\cdot\frac{}{\surd3}=\frac{8√3}{3}\frac{8}{\sqrt3}\cdot\frac{}{\surd3}=\frac{8√3}{3}\frac{8}{\sqrt3}\cdot\frac{}{\surd3}=\frac{8√3}{3}\frac{8}{\sqrt3}\cdot\frac{\surd}{\surd3}=\frac{8√3}{3}\frac{8}{\sqrt3}\cdot\frac{√3}{√3}=\frac{8√3}{3}\frac{8}{\sqrt3}\frac{√3}{√3}=\frac{8√3}{3}\frac{8}{\sqrt3}\frac{√3}{√3}=\frac{8√3}{3}\frac{8}{\sqrt3}\frac{√3}{√3}=\frac{8√3}{3}\frac{8}{\sqrt3}\frac{√3}{√3}=\frac{8√3}{3}\frac{8}{\sqrt3}\frac{√3}{√3}=\frac{8√3}{3}\frac{8}{\sqrt3}\frac{√3}{√3}=\frac{8√3}{3}\frac{8}{\sqrt3}\times\frac{√3}{√3}=\frac{8√3}{3}\frac{8}{\sqrt33}\times\frac{√3}{√3}=\frac{8√3}{3}\frac83\times\frac{√3}{√3}=\frac{8√3}{3}\frac83\times\frac{√3}{√3}=\frac{8√3}{3}\frac83\times\frac{√3}{√3}=\frac{8√3}{3}\frac83\times\frac{√3}{√3}=\frac{8√3}{3}\frac83\times\frac{√3}{√3}=\frac{8√3}{3}\frac83\times\frac{√3}{√3}=\frac{8√3}{3}\frac83\times\frac{√3}{√3}=\frac{8√3}{3}\frac83\times\frac{√3}{√3}=\frac{8√3}{3}\frac83\times\frac{√3}{√3}=\frac{8√3}{3}\frac83\times\frac{√3}{√3}=\frac{8√3}{3}\frac83\times\frac{√3}{√3}=\frac{8√3}{3}\frac{8}{√3} × \frac{√3}{√3} = \frac{8√3}{3}\frac{8}{√3} × \frac{√3}{√3} = \frac{8√3}{3}rrrrr\frac{\placeholder{}}{\placeholder{}}
Voorbeeld 2: Herleid \sqrt{2\frac45}\sqrt{\frac45}\sqrt{\frac{4}{\placeholder{}}}\sqrt{\frac{\placeholder{}}{\placeholder{}}}\sqrt{\placeholder{}}
Zet2\frac45\frac45\frac{4}{\placeholder{}}\frac{\placeholder{}}{\placeholder{}}eerst om in een breuk: 2\frac45=\frac{14}{5}\Rightarrow\frac{\sqrt{14}}{\sqrt5}=\frac{\sqrt{14}}{\sqrt5}\cdot\frac{\sqrt5}{\sqrt5}=\frac{\sqrt{70}}{5}2\frac45=\frac{14}{5}\Rightarrow\frac{\sqrt{14}}{\sqrt5}=\frac{\sqrt{14}}{\sqrt5}\cdot\frac{\sqrt5}{\sqrt5}=\frac{}{5}2\frac45=\frac{14}{5}\Rightarrow\frac{\sqrt{14}}{\sqrt5}=\frac{\sqrt{14}}{\sqrt5}\cdot\frac{\sqrt5}{\sqrt5}=\frac{}{5}2\frac45=\frac{14}{5}\Rightarrow\frac{\sqrt{14}}{\sqrt5}=\frac{\sqrt{14}}{\sqrt5}\cdot\frac{\sqrt5}{\sqrt5}=\frac{}{5}2\frac45=\frac{14}{5}\Rightarrow\frac{\sqrt{14}}{\sqrt5}=\frac{\sqrt{14}}{\sqrt5}\cdot\frac{\sqrt5}{\sqrt5}=\frac{}{5}2\frac45=\frac{14}{5}\Rightarrow\frac{\sqrt{14}}{\sqrt5}=\frac{\sqrt{14}}{\sqrt5}\cdot\frac{\sqrt5}{\sqrt5}=\frac{}{5}2\frac45=\frac{14}{5}\Rightarrow\frac{\sqrt{14}}{\sqrt5}=\frac{\sqrt{14}}{\sqrt5}\cdot\frac{\sqrt5}{\sqrt5}=\frac{}{5}2\frac45=\frac{14}{5}\Rightarrow\frac{\sqrt{14}}{\sqrt5}=\frac{\sqrt{14}}{\sqrt5}\cdot\frac{\sqrt5}{\sqrt5}=\frac{}{5}2\frac45=\frac{14}{5}\Rightarrow\frac{\sqrt{14}}{\sqrt5}=\frac{\sqrt{14}}{\sqrt5}\cdot\frac{\sqrt5}{\sqrt5}=\frac{}{5}2\frac45=\frac{14}{5}\Rightarrow\frac{\sqrt{14}}{\sqrt5}=\frac{\sqrt{14}}{\sqrt5}\cdot\frac{\sqrt5}{\sqrt5}=\frac{}{5}2\frac45=\frac{14}{5}\Rightarrow\frac{\sqrt{14}}{\sqrt5}=\frac{\sqrt{14}}{\sqrt5}\cdot\frac{\sqrt5}{\sqrt5}=\frac{}{5}2\frac45=\frac{14}{5}\Rightarrow\frac{\sqrt{14}}{\sqrt5}=\frac{\sqrt{14}}{\sqrt5}\cdot\frac{\sqrt5}{\sqrt5}=\frac{\surd}{5}2\frac45=\frac{14}{5}\Rightarrow\frac{\sqrt{14}}{\sqrt5}=\frac{\sqrt{14}}{\sqrt5}\cdot\frac{\sqrt5}{\sqrt5}=\frac{\surd7}{5}2\frac45=\frac{14}{5}\Rightarrow\frac{\sqrt{14}}{\sqrt5}=\frac{\sqrt{14}}{\sqrt5}\cdot\frac{\sqrt5}{\sqrt5}=\frac{√70}{5}2\frac45=\frac{14}{5}\Rightarrow\frac{\sqrt{14}}{\sqrt5}=\frac{\sqrt{14}}{\sqrt5}\cdot\frac{\sqrt5}{}=\frac{√70}{5}2\frac45=\frac{14}{5}\Rightarrow\frac{\sqrt{14}}{\sqrt5}=\frac{\sqrt{14}}{\sqrt5}\cdot\frac{\sqrt5}{}=\frac{√70}{5}2\frac45=\frac{14}{5}\Rightarrow\frac{\sqrt{14}}{\sqrt5}=\frac{\sqrt{14}}{\sqrt5}\cdot\frac{\sqrt5}{}=\frac{√70}{5}2\frac45=\frac{14}{5}\Rightarrow\frac{\sqrt{14}}{\sqrt5}=\frac{\sqrt{14}}{\sqrt5}\cdot\frac{\sqrt5}{}=\frac{√70}{5}2\frac45=\frac{14}{5}\Rightarrow\frac{\sqrt{14}}{\sqrt5}=\frac{\sqrt{14}}{\sqrt5}\cdot\frac{\sqrt5}{}=\frac{√70}{5}2\frac45=\frac{14}{5}\Rightarrow\frac{\sqrt{14}}{\sqrt5}=\frac{\sqrt{14}}{\sqrt5}\cdot\frac{\sqrt5}{}=\frac{√70}{5}2\frac45=\frac{14}{5}\Rightarrow\frac{\sqrt{14}}{\sqrt5}=\frac{\sqrt{14}}{\sqrt5}\cdot\frac{\sqrt5}{}=\frac{√70}{5}2\frac45=\frac{14}{5}\Rightarrow\frac{\sqrt{14}}{\sqrt5}=\frac{\sqrt{14}}{\sqrt5}\cdot\frac{\sqrt5}{}=\frac{√70}{5}2\frac45=\frac{14}{5}\Rightarrow\frac{\sqrt{14}}{\sqrt5}=\frac{\sqrt{14}}{\sqrt5}\cdot\frac{\sqrt5}{}=\frac{√70}{5}2\frac45=\frac{14}{5}\Rightarrow\frac{\sqrt{14}}{\sqrt5}=\frac{\sqrt{14}}{\sqrt5}\cdot\frac{\sqrt5}{\surd}=\frac{√70}{5}2\frac45=\frac{14}{5}\Rightarrow\frac{\sqrt{14}}{\sqrt5}=\frac{\sqrt{14}}{\sqrt5}\cdot\frac{\sqrt5}{\surd5}=\frac{√70}{5}2\frac45=\frac{14}{5}\Rightarrow\frac{\sqrt{14}}{\sqrt5}=\frac{\sqrt{14}}{\sqrt5}\cdot\frac{}{\surd5}=\frac{√70}{5}2\frac45=\frac{14}{5}\Rightarrow\frac{\sqrt{14}}{\sqrt5}=\frac{\sqrt{14}}{\sqrt5}\cdot\frac{}{\surd5}=\frac{√70}{5}2\frac45=\frac{14}{5}\Rightarrow\frac{\sqrt{14}}{\sqrt5}=\frac{\sqrt{14}}{\sqrt5}\cdot\frac{}{\surd5}=\frac{√70}{5}2\frac45=\frac{14}{5}\Rightarrow\frac{\sqrt{14}}{\sqrt5}=\frac{\sqrt{14}}{\sqrt5}\cdot\frac{}{\surd5}=\frac{√70}{5}2\frac45=\frac{14}{5}\Rightarrow\frac{\sqrt{14}}{\sqrt5}=\frac{\sqrt{14}}{\sqrt5}\cdot\frac{}{\surd5}=\frac{√70}{5}2\frac45=\frac{14}{5}\Rightarrow\frac{\sqrt{14}}{\sqrt5}=\frac{\sqrt{14}}{\sqrt5}\cdot\frac{}{\surd5}=\frac{√70}{5}2\frac45=\frac{14}{5}\Rightarrow\frac{\sqrt{14}}{\sqrt5}=\frac{\sqrt{14}}{\sqrt5}\cdot\frac{}{\surd5}=\frac{√70}{5}2\frac45=\frac{14}{5}\Rightarrow\frac{\sqrt{14}}{\sqrt5}=\frac{\sqrt{14}}{\sqrt5}\cdot\frac{}{\surd5}=\frac{√70}{5}2\frac45=\frac{14}{5}\Rightarrow\frac{\sqrt{14}}{\sqrt5}=\frac{\sqrt{14}}{\sqrt5}\cdot\frac{}{\surd5}=\frac{√70}{5}2\frac45=\frac{14}{5}\Rightarrow\frac{\sqrt{14}}{\sqrt5}=\frac{\sqrt{14}}{\sqrt5}\cdot\frac{\surd}{\surd5}=\frac{√70}{5}2\frac45=\frac{14}{5}\Rightarrow\frac{\sqrt{14}}{\sqrt5}=\frac{\sqrt{14}}{\sqrt5}\cdot\frac{√5}{√5}=\frac{√70}{5}2\frac45=\frac{14}{5}\Rightarrow\frac{\sqrt{14}}{\sqrt5}=\frac{\sqrt{14}}{\sqrt5}\frac{√5}{√5}=\frac{√70}{5}2\frac45=\frac{14}{5}\Rightarrow\frac{\sqrt{14}}{\sqrt5}=\frac{\sqrt{14}}{\sqrt5}\frac{√5}{√5}=\frac{√70}{5}2\frac45=\frac{14}{5}\Rightarrow\frac{\sqrt{14}}{\sqrt5}=\frac{\sqrt{14}}{\sqrt5}\frac{√5}{√5}=\frac{√70}{5}2\frac45=\frac{14}{5}\Rightarrow\frac{\sqrt{14}}{\sqrt5}=\frac{\sqrt{14}}{\sqrt5}\frac{√5}{√5}=\frac{√70}{5}2\frac45=\frac{14}{5}\Rightarrow\frac{\sqrt{14}}{\sqrt5}=\frac{\sqrt{14}}{\sqrt5}\frac{√5}{√5}=\frac{√70}{5}2\frac45=\frac{14}{5}\Rightarrow\frac{\sqrt{14}}{\sqrt5}=\frac{\sqrt{14}}{\sqrt5}\frac{√5}{√5}=\frac{√70}{5}2\frac45=\frac{14}{5}\Rightarrow\frac{\sqrt{14}}{\sqrt5}=\frac{\sqrt{14}}{\sqrt5}\times\frac{√5}{√5}=\frac{√70}{5}2\frac45=\frac{14}{5}\Rightarrow\frac{\sqrt{14}}{\sqrt5}=\frac{\sqrt{14}}{\sqrt5}\times\surd5\surd5=\frac{√70}{5}2\frac45=\frac{14}{5}\Rightarrow\frac{\sqrt{14}}{\sqrt5}=\frac{\sqrt{14}}{\sqrt5}\times\frac{√5}{√5}=\frac{√70}{5}2\frac45=\frac{14}{5}\Rightarrow\frac{\sqrt{14}}{\sqrt5}=\frac{\sqrt{14}}{}\times\frac{√5}{√5}=\frac{√70}{5}2\frac45=\frac{14}{5}\Rightarrow\frac{\sqrt{14}}{\sqrt5}=\frac{\sqrt{14}}{}\times\frac{√5}{√5}=\frac{√70}{5}2\frac45=\frac{14}{5}\Rightarrow\frac{\sqrt{14}}{\sqrt5}=\frac{\sqrt{14}}{}\times\frac{√5}{√5}=\frac{√70}{5}2\frac45=\frac{14}{5}\Rightarrow\frac{\sqrt{14}}{\sqrt5}=\frac{\sqrt{14}}{}\times\frac{√5}{√5}=\frac{√70}{5}2\frac45=\frac{14}{5}\Rightarrow\frac{\sqrt{14}}{\sqrt5}=\frac{\sqrt{14}}{}\times\frac{√5}{√5}=\frac{√70}{5}2\frac45=\frac{14}{5}\Rightarrow\frac{\sqrt{14}}{\sqrt5}=\frac{\sqrt{14}}{}\times\frac{√5}{√5}=\frac{√70}{5}2\frac45=\frac{14}{5}\Rightarrow\frac{\sqrt{14}}{\sqrt5}=\frac{\sqrt{14}}{}\times\frac{√5}{√5}=\frac{√70}{5}2\frac45=\frac{14}{5}\Rightarrow\frac{\sqrt{14}}{\sqrt5}=\frac{\sqrt{14}}{}\times\frac{√5}{√5}=\frac{√70}{5}2\frac45=\frac{14}{5}\Rightarrow\frac{\sqrt{14}}{\sqrt5}=\frac{\sqrt{14}}{}\times\frac{√5}{√5}=\frac{√70}{5}2\frac45=\frac{14}{5}\Rightarrow\frac{\sqrt{14}}{\sqrt5}=\frac{\sqrt{14}}{\surd}\times\frac{√5}{√5}=\frac{√70}{5}2\frac45=\frac{14}{5}\Rightarrow\frac{\sqrt{14}}{\sqrt5}=\frac{\sqrt{14}}{\surd5}\times\frac{√5}{√5}=\frac{√70}{5}2\frac45=\frac{14}{5}\Rightarrow\frac{\sqrt{14}}{\sqrt5}=\frac{}{\surd5}\times\frac{√5}{√5}=\frac{√70}{5}2\frac45=\frac{14}{5}\Rightarrow\frac{\sqrt{14}}{\sqrt5}=\frac{}{\surd5}\times\frac{√5}{√5}=\frac{√70}{5}2\frac45=\frac{14}{5}\Rightarrow\frac{\sqrt{14}}{\sqrt5}=\frac{}{\surd5}\times\frac{√5}{√5}=\frac{√70}{5}2\frac45=\frac{14}{5}\Rightarrow\frac{\sqrt{14}}{\sqrt5}=\frac{}{\surd5}\times\frac{√5}{√5}=\frac{√70}{5}2\frac45=\frac{14}{5}\Rightarrow\frac{\sqrt{14}}{\sqrt5}=\frac{}{\surd5}\times\frac{√5}{√5}=\frac{√70}{5}2\frac45=\frac{14}{5}\Rightarrow\frac{\sqrt{14}}{\sqrt5}=\frac{}{\surd5}\times\frac{√5}{√5}=\frac{√70}{5}2\frac45=\frac{14}{5}\Rightarrow\frac{\sqrt{14}}{\sqrt5}=\frac{}{\surd5}\times\frac{√5}{√5}=\frac{√70}{5}2\frac45=\frac{14}{5}\Rightarrow\frac{\sqrt{14}}{\sqrt5}=\frac{}{\surd5}\times\frac{√5}{√5}=\frac{√70}{5}2\frac45=\frac{14}{5}\Rightarrow\frac{\sqrt{14}}{\sqrt5}=\frac{}{\surd5}\times\frac{√5}{√5}=\frac{√70}{5}2\frac45=\frac{14}{5}\Rightarrow\frac{\sqrt{14}}{\sqrt5}=\frac{}{\surd5}\times\frac{√5}{√5}=\frac{√70}{5}2\frac45=\frac{14}{5}\Rightarrow\frac{\sqrt{14}}{\sqrt5}=\frac{\surd}{\surd5}\times\frac{√5}{√5}=\frac{√70}{5}2\frac45=\frac{14}{5}\Rightarrow\frac{\sqrt{14}}{\sqrt5}=\frac{\surd1}{\surd5}\times\frac{√5}{√5}=\frac{√70}{5}2\frac45=\frac{14}{5}\Rightarrow\frac{\sqrt{14}}{\sqrt5}=\frac{√14}{√5}\times\frac{√5}{√5}=\frac{√70}{5}2\frac45=\frac{14}{5}\Rightarrow\frac{\sqrt{14}}{}=\frac{√14}{√5}\times\frac{√5}{√5}=\frac{√70}{5}2\frac45=\frac{14}{5}\Rightarrow\frac{\sqrt{14}}{}=\frac{√14}{√5}\times\frac{√5}{√5}=\frac{√70}{5}2\frac45=\frac{14}{5}\Rightarrow\frac{\sqrt{14}}{}=\frac{√14}{√5}\times\frac{√5}{√5}=\frac{√70}{5}2\frac45=\frac{14}{5}\Rightarrow\frac{\sqrt{14}}{}=\frac{√14}{√5}\times\frac{√5}{√5}=\frac{√70}{5}2\frac45=\frac{14}{5}\Rightarrow\frac{\sqrt{14}}{}=\frac{√14}{√5}\times\frac{√5}{√5}=\frac{√70}{5}2\frac45=\frac{14}{5}\Rightarrow\frac{\sqrt{14}}{}=\frac{√14}{√5}\times\frac{√5}{√5}=\frac{√70}{5}2\frac45=\frac{14}{5}\Rightarrow\frac{\sqrt{14}}{}=\frac{√14}{√5}\times\frac{√5}{√5}=\frac{√70}{5}2\frac45=\frac{14}{5}\Rightarrow\frac{\sqrt{14}}{}=\frac{√14}{√5}\times\frac{√5}{√5}=\frac{√70}{5}2\frac45=\frac{14}{5}\Rightarrow\frac{\sqrt{14}}{}=\frac{√14}{√5}\times\frac{√5}{√5}=\frac{√70}{5}2\frac45=\frac{14}{5}\Rightarrow\frac{\sqrt{14}}{\surd}=\frac{√14}{√5}\times\frac{√5}{√5}=\frac{√70}{5}2\frac45=\frac{14}{5}\Rightarrow\frac{\sqrt{14}}{\surd5}=\frac{√14}{√5}\times\frac{√5}{√5}=\frac{√70}{5}2\frac45=\frac{14}{5}\Rightarrow\frac{}{\surd5}=\frac{√14}{√5}\times\frac{√5}{√5}=\frac{√70}{5}2\frac45=\frac{14}{5}\Rightarrow\frac{}{\surd5}=\frac{√14}{√5}\times\frac{√5}{√5}=\frac{√70}{5}2\frac45=\frac{14}{5}\Rightarrow\frac{}{\surd5}=\frac{√14}{√5}\times\frac{√5}{√5}=\frac{√70}{5}2\frac45=\frac{14}{5}\Rightarrow\frac{}{\surd5}=\frac{√14}{√5}\times\frac{√5}{√5}=\frac{√70}{5}2\frac45=\frac{14}{5}\Rightarrow\frac{}{\surd5}=\frac{√14}{√5}\times\frac{√5}{√5}=\frac{√70}{5}2\frac45=\frac{14}{5}\Rightarrow\frac{}{\surd5}=\frac{√14}{√5}\times\frac{√5}{√5}=\frac{√70}{5}2\frac45=\frac{14}{5}\Rightarrow\frac{}{\surd5}=\frac{√14}{√5}\times\frac{√5}{√5}=\frac{√70}{5}2\frac45=\frac{14}{5}\Rightarrow\frac{}{\surd5}=\frac{√14}{√5}\times\frac{√5}{√5}=\frac{√70}{5}2\frac45=\frac{14}{5}\Rightarrow\frac{}{\surd5}=\frac{√14}{√5}\times\frac{√5}{√5}=\frac{√70}{5}2\frac45=\frac{14}{5}\Rightarrow\frac{}{\surd5}=\frac{√14}{√5}\times\frac{√5}{√5}=\frac{√70}{5}2\frac45=\frac{14}{5}\Rightarrow\frac{\surd}{\surd5}=\frac{√14}{√5}\times\frac{√5}{√5}=\frac{√70}{5}2\frac45=\frac{14}{5}\Rightarrow\frac{\surd1}{\surd5}=\frac{√14}{√5}\times\frac{√5}{√5}=\frac{√70}{5}2\frac45=\frac{14}{5}\Rightarrow\frac{√14}{√5}=\frac{√14}{√5}\times\frac{√5}{√5}=\frac{√70}{5}2=\frac{14}{5}\Rightarrow\frac{√14}{√5}=\frac{√14}{√5}\times\frac{√5}{√5}=\frac{√70}{5}2=\frac{14}{5}\Rightarrow\frac{√14}{√5}=\frac{√14}{√5}\times\frac{√5}{√5}=\frac{√70}{5}2=\frac{14}{5}\Rightarrow\frac{√14}{√5}=\frac{√14}{√5}\times\frac{√5}{√5}=\frac{√70}{5}2=\frac{14}{5}\Rightarrow\frac{√14}{√5}=\frac{√14}{√5}\times\frac{√5}{√5}=\frac{√70}{5}2=\frac{14}{5}\Rightarrow\frac{√14}{√5}=\frac{√14}{√5}\times\frac{√5}{√5}=\frac{√70}{5}2=\frac{14}{5}\Rightarrow\frac{√14}{√5}=\frac{√14}{√5}\times\frac{√5}{√5}=\frac{√70}{5}2=\frac{14}{5}\Rightarrow\frac{√14}{√5}=\frac{√14}{√5}\times\frac{√5}{√5}=\frac{√70}{5}2=\frac{14}{5}\Rightarrow\frac{√14}{√5}=\frac{√14}{√5}\times\frac{√5}{√5}=\frac{√70}{5}2=\frac{14}{5}\Rightarrow\frac{√14}{√5}=\frac{√14}{√5}\times\frac{√5}{√5}=\frac{√70}{5}2=\frac{14}{5}\Rightarrow\frac{√14}{√5}=\frac{√14}{√5}\times\frac{√5}{√5}=\frac{√70}{5}2=\frac{14}{5}\Rightarrow\frac{√14}{√5}=\frac{√14}{√5}\times\frac{√5}{√5}=\frac{√70}{5}2=\frac{14}{5}\Rightarrow\frac{√14}{√5}=\frac{√14}{√5}\times\frac{√5}{√5}=\frac{√70}{5}=\frac{14}{5}\Rightarrow\frac{√14}{√5}=\frac{√14}{√5}\times\frac{√5}{√5}=\frac{√70}{5}\frac{14}{5}\Rightarrow\frac{√14}{√5}=\frac{√14}{√5}\times\frac{√5}{√5}=\frac{√70}{5}\frac{=14}{5}\Rightarrow\frac{√14}{√5}=\frac{√14}{√5}\times\frac{√5}{√5}=\frac{√70}{5}\frac{14}{5} \Rightarrow \frac{√14}{√5} = \frac{√14}{√5} × \frac{√5}{√5} = \frac{√70}{5}\frac{14}{5} \Rightarrow \frac{√14}{√5} = \frac{√14}{√5} × \frac{√5}{√5} = \frac{√70}{5}
Voorbeeld 3: Herleid \frac{10}{\sqrt2}-6\sqrt{18}\frac{10}{\sqrt2}-6\sqrt1\frac{10}{\sqrt2}-6\sqrt{\placeholder{}}\frac{10}{\sqrt2}-6\frac{10}{\sqrt2}-\frac{10}{\sqrt2}\frac{10}{\sqrt{\placeholder{}}}\frac{10}{\placeholder{}}\frac{1}{\placeholder{}}\frac{\placeholder{}}{\placeholder{}}
De eerste term: \frac{10}{\sqrt2}\cdot\frac{\sqrt2}{\sqrt2}=\frac{10\sqrt2}{2}=5\sqrt2\frac{10}{\sqrt2}\cdot\frac{\sqrt2}{\sqrt2}=\frac{10\sqrt2}{2}=5\frac{10}{\sqrt2}\cdot\frac{\sqrt2}{\sqrt2}=\frac{10\sqrt2}{2}=5\frac{10}{\sqrt2}\cdot\frac{\sqrt2}{\sqrt2}=\frac{10\sqrt2}{2}=5\frac{10}{\sqrt2}\cdot\frac{\sqrt2}{\sqrt2}=\frac{10\sqrt2}{2}=5\frac{10}{\sqrt2}\cdot\frac{\sqrt2}{\sqrt2}=\frac{10\sqrt2}{2}=5\frac{10}{\sqrt2}\cdot\frac{\sqrt2}{\sqrt2}=\frac{10\sqrt2}{2}=5\frac{10}{\sqrt2}\cdot\frac{\sqrt2}{\sqrt2}=\frac{10\sqrt2}{2}=5\frac{10}{\sqrt2}\cdot\frac{\sqrt2}{\sqrt2}=\frac{10\sqrt2}{2}=5\frac{10}{\sqrt2}\cdot\frac{\sqrt2}{\sqrt2}=\frac{10\sqrt2}{2}=5\frac{10}{\sqrt2}\cdot\frac{\sqrt2}{\sqrt2}=\frac{10\sqrt2}{2}=5\surd\frac{10}{\sqrt2}\cdot\frac{\sqrt2}{\sqrt2}=\frac{10\sqrt2}{2}=5\surd2\frac{10}{\sqrt2}\cdot\frac{\sqrt2}{\sqrt2}=\frac{10}{2}=5\surd2\frac{10}{\sqrt2}\cdot\frac{\sqrt2}{\sqrt2}=\frac{10}{2}=5\surd2\frac{10}{\sqrt2}\cdot\frac{\sqrt2}{\sqrt2}=\frac{10}{2}=5\surd2\frac{10}{\sqrt2}\cdot\frac{\sqrt2}{\sqrt2}=\frac{10}{2}=5\surd2\frac{10}{\sqrt2}\cdot\frac{\sqrt2}{\sqrt2}=\frac{10}{2}=5\surd2\frac{10}{\sqrt2}\cdot\frac{\sqrt2}{\sqrt2}=\frac{10}{2}=5\surd2\frac{10}{\sqrt2}\cdot\frac{\sqrt2}{\sqrt2}=\frac{10}{2}=5\surd2\frac{10}{\sqrt2}\cdot\frac{\sqrt2}{\sqrt2}=\frac{10}{2}=5\surd2\frac{10}{\sqrt2}\cdot\frac{\sqrt2}{\sqrt2}=\frac{10}{2}=5\surd2\frac{10}{\sqrt2}\cdot\frac{\sqrt2}{\sqrt2}=\frac{10\surd}{2}=5\surd2\frac{10}{\sqrt2}\cdot\frac{\sqrt2}{\sqrt2}=\frac{10√2}{2}=5\surd2\frac{10}{\sqrt2}\cdot\frac{\sqrt2}{}=\frac{10√2}{2}=5\surd2\frac{10}{\sqrt2}\cdot\frac{\sqrt2}{}=\frac{10√2}{2}=5\surd2\frac{10}{\sqrt2}\cdot\frac{\sqrt2}{}=\frac{10√2}{2}=5\surd2\frac{10}{\sqrt2}\cdot\frac{\sqrt2}{}=\frac{10√2}{2}=5\surd2\frac{10}{\sqrt2}\cdot\frac{\sqrt2}{}=\frac{10√2}{2}=5\surd2\frac{10}{\sqrt2}\cdot\frac{\sqrt2}{}=\frac{10√2}{2}=5\surd2\frac{10}{\sqrt2}\cdot\frac{\sqrt2}{}=\frac{10√2}{2}=5\surd2\frac{10}{\sqrt2}\cdot\frac{\sqrt2}{}=\frac{10√2}{2}=5\surd2\frac{10}{\sqrt2}\cdot\frac{\sqrt2}{}=\frac{10√2}{2}=5\surd2\frac{10}{\sqrt2}\cdot\frac{\sqrt2}{\surd}=\frac{10√2}{2}=5\surd2\frac{10}{\sqrt2}\cdot\frac{\sqrt2}{\surd2}=\frac{10√2}{2}=5\surd2\frac{10}{\sqrt2}\cdot\frac{}{\surd2}=\frac{10√2}{2}=5\surd2\frac{10}{\sqrt2}\cdot\frac{}{\surd2}=\frac{10√2}{2}=5\surd2\frac{10}{\sqrt2}\cdot\frac{}{\surd2}=\frac{10√2}{2}=5\surd2\frac{10}{\sqrt2}\cdot\frac{}{\surd2}=\frac{10√2}{2}=5\surd2\frac{10}{\sqrt2}\cdot\frac{}{\surd2}=\frac{10√2}{2}=5\surd2\frac{10}{\sqrt2}\cdot\frac{}{\surd2}=\frac{10√2}{2}=5\surd2\frac{10}{\sqrt2}\cdot\frac{}{\surd2}=\frac{10√2}{2}=5\surd2\frac{10}{\sqrt2}\cdot\frac{}{\surd2}=\frac{10√2}{2}=5\surd2\frac{10}{\sqrt2}\cdot\frac{}{\surd2}=\frac{10√2}{2}=5\surd2\frac{10}{\sqrt2}\cdot\frac{\surd}{\surd2}=\frac{10√2}{2}=5\surd2\frac{10}{\sqrt2}\cdot\frac{√2}{√2}=\frac{10√2}{2}=5\surd2\frac{10}{\sqrt2}\frac{√2}{√2}=\frac{10√2}{2}=5\surd2\frac{10}{\sqrt2}\frac{√2}{√2}=\frac{10√2}{2}=5\surd2\frac{10}{\sqrt2}\frac{√2}{√2}=\frac{10√2}{2}=5\surd2\frac{10}{\sqrt2}\frac{√2}{√2}=\frac{10√2}{2}=5\surd2\frac{10}{\sqrt2}\frac{√2}{√2}=\frac{10√2}{2}=5\surd2\frac{10}{\sqrt2}\frac{√2}{√2}=\frac{10√2}{2}=5\surd2\frac{10}{\sqrt2}\times\frac{√2}{√2}=\frac{10√2}{2}=5\surd2\frac{10}{}\times\frac{√2}{√2}=\frac{10√2}{2}=5\surd2\frac{10}{}\times\frac{√2}{√2}=\frac{10√2}{2}=5\surd2\frac{10}{}\times\frac{√2}{√2}=\frac{10√2}{2}=5\surd2\frac{10}{}\times\frac{√2}{√2}=\frac{10√2}{2}=5\surd2\frac{10}{}\times\frac{√2}{√2}=\frac{10√2}{2}=5\surd2\frac{10}{}\times\frac{√2}{√2}=\frac{10√2}{2}=5\surd2\frac{10}{}\times\frac{√2}{√2}=\frac{10√2}{2}=5\surd2\frac{10}{}\times\frac{√2}{√2}=\frac{10√2}{2}=5\surd2\frac{10}{}\times\frac{√2}{√2}=\frac{10√2}{2}=5\surd2\frac{10}{\surd}\times\frac{√2}{√2}=\frac{10√2}{2}=5\surd2\frac{10}{√2} × \frac{√2}{√2} = \frac{10√2}{2}= 5√2\frac{10}{√2} × \frac{√2}{√2} = \frac{10√2}{2}= 5√2
De tweede term:
-6\sqrt{18}=-6\cdot\sqrt{9\cdot2}=-6\times3\sqrt2=-18\sqrt2-6\sqrt{18}=-6\cdot\sqrt{9\cdot2}=-6\times3\sqrt2=-18-6\sqrt{18}=-6\cdot\sqrt{9\cdot2}=-6\times3\sqrt2=-18-6\sqrt{18}=-6\cdot\sqrt{9\cdot2}=-6\times3\sqrt2=-18-6\sqrt{18}=-6\cdot\sqrt{9\cdot2}=-6\times3\sqrt2=-18-6\sqrt{18}=-6\cdot\sqrt{9\cdot2}=-6\times3\sqrt2=-18-6\sqrt{18}=-6\cdot\sqrt{9\cdot2}=-6\times3\sqrt2=-18-6\sqrt{18}=-6\cdot\sqrt{9\cdot2}=-6\times3\sqrt2=-18-6\sqrt{18}=-6\cdot\sqrt{9\cdot2}=-6\times3\sqrt2=-18-6\sqrt{18}=-6\cdot\sqrt{9\cdot2}=-6\times3\sqrt2=-18-6\sqrt{18}=-6\cdot\sqrt{9\cdot2}=-6\times3\sqrt2=-18\surd-6\sqrt{18}=-6\cdot\sqrt{9\cdot2}=-6\times3\sqrt2=-18\surd2-6\sqrt{18}=-6\cdot\sqrt{9\cdot2}=-6\times3=-18\surd2-6\sqrt{18}=-6\cdot\sqrt{9\cdot2}=-6\times3=-18\surd2-6\sqrt{18}=-6\cdot\sqrt{9\cdot2}=-6\times3=-18\surd2-6\sqrt{18}=-6\cdot\sqrt{9\cdot2}=-6\times3=-18\surd2-6\sqrt{18}=-6\cdot\sqrt{9\cdot2}=-6\times3=-18\surd2-6\sqrt{18}=-6\cdot\sqrt{9\cdot2}=-6\times3=-18\surd2-6\sqrt{18}=-6\cdot\sqrt{9\cdot2}=-6\times3=-18\surd2-6\sqrt{18}=-6\cdot\sqrt{9\cdot2}=-6\times3=-18\surd2-6\sqrt{18}=-6\cdot\sqrt{9\cdot2}=-6\times3=-18\surd2-6\sqrt{18}=-6\cdot\sqrt{9\cdot2}=-6\times3\surd=-18\surd2-6\sqrt{18}=-6\cdot\sqrt{9\cdot2}=-6\times3\surd2=-18\surd2-6\sqrt{18}=-6\cdot=-6\times3\surd2=-18\surd2-6\sqrt{18}=-6\cdot=-6\times3\surd2=-18\surd2-6\sqrt{18}=-6\cdot=-6\times3\surd2=-18\surd2-6\sqrt{18}=-6\cdot=-6\times3\surd2=-18\surd2-6\sqrt{18}=-6\cdot=-6\times3\surd2=-18\surd2-6\sqrt{18}=-6\cdot=-6\times3\surd2=-18\surd2-6\sqrt{18}=-6\cdot=-6\times3\surd2=-18\surd2-6\sqrt{18}=-6\cdot=-6\times3\surd2=-18\surd2-6\sqrt{18}=-6\cdot=-6\times3\surd2=-18\surd2-6\sqrt{18}=-6\cdot=-6\times3\surd2=-18\surd2-6\sqrt{18}=-6\cdot=-6\times3\surd2=-18\surd2-6\sqrt{18}=-6\cdot=-6\times3\surd2=-18\surd2-6\sqrt{18}=-6\cdot=-6\times3\surd2=-18\surd2-6\sqrt{18}=-6\cdot=-6\times3\surd2=-18\surd2-6\sqrt{18}=-6\cdot=-6\times3\surd2=-18\surd2-6\sqrt{18}=-6\cdot\surd=-6\times3\surd2=-18\surd2-6\sqrt{18}=-6\cdot\surd(=-6\times3\surd2=-18\surd2-6\sqrt{18}=-6\cdot\surd(9=-6\times3\surd2=-18\surd2-6\sqrt{18}=-6\cdot\surd(9\times=-6\times3\surd2=-18\surd2-6\sqrt{18}=-6\cdot\surd(9\times2=-6\times3\surd2=-18\surd2-6\sqrt{18}=-6\cdot\surd(9\times2)=-6\times3\surd2=-18\surd2-6\sqrt{18}=-6\surd(9\times2)=-6\times3\surd2=-18\surd2-6\sqrt{18}=-6\surd(9\times2)=-6\times3\surd2=-18\surd2-6\sqrt{18}=-6\surd(9\times2)=-6\times3\surd2=-18\surd2-6\sqrt{18}=-6\surd(9\times2)=-6\times3\surd2=-18\surd2-6\sqrt{18}=-6\surd(9\times2)=-6\times3\surd2=-18\surd2-6\sqrt{18}=-6\surd(9\times2)=-6\times3\surd2=-18\surd2-6\sqrt{18}=-6\times\surd(9\times2)=-6\times3\surd2=-18\surd2-6=-6\times\surd(9\times2)=-6\times3\surd2=-18\surd2-6=-6\times\surd(9\times2)=-6\times3\surd2=-18\surd2-6=-6\times\surd(9\times2)=-6\times3\surd2=-18\surd2-6=-6\times\surd(9\times2)=-6\times3\surd2=-18\surd2-6=-6\times\surd(9\times2)=-6\times3\surd2=-18\surd2-6=-6\times\surd(9\times2)=-6\times3\surd2=-18\surd2-6=-6\times\surd(9\times2)=-6\times3\surd2=-18\surd2-6=-6\times\surd(9\times2)=-6\times3\surd2=-18\surd2-6=-6\times\surd(9\times2)=-6\times3\surd2=-18\surd2-6=-6\times\surd(9\times2)=-6\times3\surd2=-18\surd2-6\surd=-6\times\surd(9\times2)=-6\times3\surd2=-18\surd2-6\surd1=-6\times\surd(9\times2)=-6\times3\surd2=-18\surd2-6 √18 = -6 × √(9 × 2) = -6 × 3 √2 = -18 √2-6 √18 = -6 × √(9 × 2) = -6 × 3 √2 = -18 √2
Samenvoegen geeft:
5\sqrt2-18\sqrt2=-13\sqrt25\sqrt2-18\sqrt2=-135\sqrt2-18\sqrt2=-135\sqrt2-18\sqrt2=-135\sqrt2-18\sqrt2=-135\sqrt2-18\sqrt2=-135\sqrt2-18\sqrt2=-135\sqrt2-18\sqrt2=-135\sqrt2-18\sqrt2=-135\sqrt2-18\sqrt2=-135\sqrt2-18\sqrt2=-13\surd5\sqrt2-18\sqrt2=-13\surd25\sqrt2-18=-13\surd25\sqrt2-18=-13\surd25\sqrt2-18=-13\surd25\sqrt2-18=-13\surd25\sqrt2-18=-13\surd25\sqrt2-18=-13\surd25\sqrt2-18=-13\surd25\sqrt2-18=-13\surd25\sqrt2-18=-13\surd25\sqrt2-18\surd=-13\surd25\sqrt2-18\surd2=-13\surd25-18\surd2=-13\surd25-18\surd2=-13\surd25-18\surd2=-13\surd25-18\surd2=-13\surd25-18\surd2=-13\surd25-18\surd2=-13\surd25-18\surd2=-13\surd25-18\surd2=-13\surd25-18\surd2=-13\surd25\surd-18\surd2=-13\surd25√2 - 18√2 = -13√25√2 - 18√2 = -13√2
