Wortels vereenvoudigen

\(\sqrt{7\frac{1}{9}}=\sqrt{\frac{64}{9}}={\sqrt{64} \over \sqrt{9}}=\frac{8}{3}=2\frac{2}{3}\text{.}\)

\(\sqrt{\frac{99}{100}}={\sqrt{99} \over \sqrt{100}}={\sqrt{99} \over 10}=\frac{1}{10}\sqrt{99}=\frac{1}{10}⋅3⋅\sqrt{11}=\frac{3}{10}\sqrt{11}\text{.}\)

\(\sqrt{\frac{25}{62}}={\sqrt{25} \over \sqrt{62}}={5 \over \sqrt{62}}⋅{\sqrt{62} \over \sqrt{62}}={5\sqrt{62} \over 62}=\frac{5}{62}\sqrt{62}\text{.}\)

\(\sqrt{1\frac{3}{5}}=\sqrt{\frac{8}{5}}={\sqrt{8} \over \sqrt{5}}⋅{\sqrt{5} \over \sqrt{5}}={\sqrt{40} \over 5}=\frac{1}{5}\sqrt{40}=\frac{1}{5}⋅2⋅\sqrt{10}=\frac{2}{5}\sqrt{10}\text{.}\)

\({6\sqrt{72} \over 3\sqrt{6}}={6 \over 3}⋅{\sqrt{72} \over \sqrt{6}}=2\sqrt{12}=2⋅\sqrt{4}⋅\sqrt{3}=2⋅2⋅\sqrt{3}=4\sqrt{3}\)

\(\sqrt{112}=\sqrt{16}⋅\sqrt{7}=4\sqrt{7}\text{.}\)

\(4\sqrt{175}=4⋅\sqrt{25}⋅\sqrt{7}=4⋅5⋅\sqrt{7}=20\sqrt{7}\text{.}\)

\(\sqrt{8}+\sqrt{50}=\sqrt{4}⋅\sqrt{2}+\sqrt{25}⋅\sqrt{2}=2\sqrt{2}+5\sqrt{2}\text{.}\)

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

\(6\sqrt{18}-4\sqrt{50}=6⋅\sqrt{9}⋅\sqrt{2}-4⋅\sqrt{25}⋅\sqrt{2}\text{.}\)

\(6⋅3⋅\sqrt{2}-4⋅5⋅\sqrt{2}=18\sqrt{2}-20\sqrt{2}=-2\sqrt{2}\text{.}\)

\({-5 \over 1-\sqrt{3}}={-5 \over 1-\sqrt{3}}⋅{1+\sqrt{3} \over 1+\sqrt{3}}\)
\(\text{}={-5(1-\sqrt{3}) \over 1-3}\)
\(\text{}=2\frac{1}{2}(1-\sqrt{3})\)
\(\text{}=2\frac{1}{2}-2\frac{1}{2}\sqrt{3}\)

\({\sqrt{6} \over \sqrt{2}-\sqrt{5}}={\sqrt{6} \over \sqrt{2}-\sqrt{5}}⋅{\sqrt{2}+\sqrt{5} \over \sqrt{2}+\sqrt{5}}\)
\(\text{}={\sqrt{6}(\sqrt{2}+\sqrt{5}) \over 2-5}\)
\(\text{}=-\frac{1}{3}\sqrt{6}(\sqrt{2}+\sqrt{5})\)
\(\text{}=-\frac{1}{3}\sqrt{12}-\frac{1}{3}\sqrt{30}\)
\(\text{}=-\frac{2}{3}\sqrt{3}-\frac{1}{3}\sqrt{30}\)

\(2\sqrt{2}⋅4\sqrt{14}=8\sqrt{28}=8⋅\sqrt{4}⋅\sqrt{7}=8⋅2⋅\sqrt{7}=16\sqrt{7}\)

\({8 \over 7\sqrt{3}}={8 \over 7\sqrt{3}}⋅{\sqrt{3} \over \sqrt{3}}={8\sqrt{3} \over 7⋅3}=\frac{8}{21}\sqrt{3}\text{.}\)