Wortels vereenvoudigen

\(\sqrt{\frac{1}{81}}={\sqrt{1} \over \sqrt{81}}=\frac{1}{9}\text{.}\)

\(\sqrt{\frac{37}{81}}={\sqrt{37} \over \sqrt{81}}={\sqrt{37} \over 9}=\frac{1}{9}\sqrt{37}\text{.}\)

\(\sqrt{1\frac{1}{24}}=\sqrt{\frac{25}{24}}={\sqrt{25} \over \sqrt{24}}={5 \over \sqrt{24}}⋅{\sqrt{24} \over \sqrt{24}}={5\sqrt{24} \over 24}=\frac{5}{24}\sqrt{24}=\frac{5}{24}⋅2⋅\sqrt{6}=\frac{5}{12}\sqrt{6}\text{.}\)

\(\sqrt{7\frac{2}{3}}=\sqrt{\frac{23}{3}}={\sqrt{23} \over \sqrt{3}}⋅{\sqrt{3} \over \sqrt{3}}={\sqrt{69} \over 3}=\frac{1}{3}\sqrt{69}\text{.}\)

\({12\sqrt{120} \over 4\sqrt{5}}={12 \over 4}⋅{\sqrt{120} \over \sqrt{5}}=3\sqrt{24}=3⋅\sqrt{4}⋅\sqrt{6}=3⋅2⋅\sqrt{6}=6\sqrt{6}\)

\(\sqrt{20}=\sqrt{4}⋅\sqrt{5}=2\sqrt{5}\text{.}\)

\(-5\sqrt{12}=-5⋅\sqrt{4}⋅\sqrt{3}=-5⋅2⋅\sqrt{3}=-10\sqrt{3}\text{.}\)

\(\sqrt{12}+\sqrt{75}=\sqrt{4}⋅\sqrt{3}+\sqrt{25}⋅\sqrt{3}=2\sqrt{3}+5\sqrt{3}\text{.}\)

\(2\sqrt{3}+5\sqrt{3}=7\sqrt{3}\text{.}\)

\(6\sqrt{500}+3\sqrt{45}=6⋅\sqrt{100}⋅\sqrt{5}+3⋅\sqrt{9}⋅\sqrt{5}\text{.}\)

\(6⋅10⋅\sqrt{5}+3⋅3⋅\sqrt{5}=60\sqrt{5}+9\sqrt{5}=69\sqrt{5}\text{.}\)

\({5 \over 6+\sqrt{3}}={5 \over 6+\sqrt{3}}⋅{6-\sqrt{3} \over 6-\sqrt{3}}\)
\(\text{}={5(6+\sqrt{3}) \over 36-3}\)
\(\text{}=\frac{5}{33}(6+\sqrt{3})\)
\(\text{}=\frac{10}{11}+\frac{5}{33}\sqrt{3}\)

\({\sqrt{5} \over \sqrt{2}+\sqrt{6}}={\sqrt{5} \over \sqrt{2}+\sqrt{6}}⋅{\sqrt{2}-\sqrt{6} \over \sqrt{2}-\sqrt{6}}\)
\(\text{}={\sqrt{5}(\sqrt{2}-\sqrt{6}) \over 2-6}\)
\(\text{}=-\frac{1}{4}\sqrt{5}(\sqrt{2}-\sqrt{6})\)
\(\text{}=-\frac{1}{4}\sqrt{10}+\frac{1}{4}\sqrt{30}\)

\(2\sqrt{6}⋅5\sqrt{2}=10\sqrt{12}=10⋅\sqrt{4}⋅\sqrt{3}=10⋅2⋅\sqrt{3}=20\sqrt{3}\)

\({5 \over 2\sqrt{5}}={5 \over 2\sqrt{5}}⋅{\sqrt{5} \over \sqrt{5}}={5\sqrt{5} \over 2⋅5}=\frac{1}{2}\sqrt{5}\text{.}\)