Wortels vereenvoudigen

\(\sqrt{2\frac{2}{49}}=\sqrt{\frac{100}{49}}={\sqrt{100} \over \sqrt{49}}=\frac{10}{7}=1\frac{3}{7}\text{.}\)

\(\sqrt{\frac{68}{81}}={\sqrt{68} \over \sqrt{81}}={\sqrt{68} \over 9}=\frac{1}{9}\sqrt{68}=\frac{1}{9}⋅2⋅\sqrt{17}=\frac{2}{9}\sqrt{17}\text{.}\)

\(\sqrt{1\frac{37}{63}}=\sqrt{\frac{100}{63}}={\sqrt{100} \over \sqrt{63}}={10 \over \sqrt{63}}⋅{\sqrt{63} \over \sqrt{63}}={10\sqrt{63} \over 63}=\frac{10}{63}\sqrt{63}=\frac{10}{63}⋅3⋅\sqrt{7}=\frac{10}{21}\sqrt{7}\text{.}\)

\(\sqrt{\frac{2}{11}}={\sqrt{2} \over \sqrt{11}}⋅{\sqrt{11} \over \sqrt{11}}={\sqrt{22} \over 11}=\frac{1}{11}\sqrt{22}\text{.}\)

\({56\sqrt{80} \over 8\sqrt{2}}={56 \over 8}⋅{\sqrt{80} \over \sqrt{2}}=7\sqrt{40}=7⋅\sqrt{4}⋅\sqrt{10}=7⋅2⋅\sqrt{10}=14\sqrt{10}\)

\(\sqrt{300}=\sqrt{100}⋅\sqrt{3}=10\sqrt{3}\text{.}\)

\(-7\sqrt{175}=-7⋅\sqrt{25}⋅\sqrt{7}=-7⋅5⋅\sqrt{7}=-35\sqrt{7}\text{.}\)

\(\sqrt{300}+\sqrt{75}=\sqrt{100}⋅\sqrt{3}+\sqrt{25}⋅\sqrt{3}=10\sqrt{3}+5\sqrt{3}\text{.}\)

\(10\sqrt{3}+5\sqrt{3}=15\sqrt{3}\text{.}\)

\(5\sqrt{500}-6\sqrt{80}=5⋅\sqrt{100}⋅\sqrt{5}-6⋅\sqrt{16}⋅\sqrt{5}\text{.}\)

\(5⋅10⋅\sqrt{5}-6⋅4⋅\sqrt{5}=50\sqrt{5}-24\sqrt{5}=26\sqrt{5}\text{.}\)

\({-4 \over 6-\sqrt{5}}={-4 \over 6-\sqrt{5}}⋅{6+\sqrt{5} \over 6+\sqrt{5}}\)
\(\text{}={-4(6-\sqrt{5}) \over 36-5}\)
\(\text{}=-\frac{4}{31}(6-\sqrt{5})\)
\(\text{}=-\frac{24}{31}+\frac{4}{31}\sqrt{5}\)

\({\sqrt{2} \over \sqrt{6}+\sqrt{5}}={\sqrt{2} \over \sqrt{6}+\sqrt{5}}⋅{\sqrt{6}-\sqrt{5} \over \sqrt{6}-\sqrt{5}}\)
\(\text{}={\sqrt{2}(\sqrt{6}-\sqrt{5}) \over 6-5}\)
\(\text{}=\sqrt{2}(\sqrt{6}-\sqrt{5})\)
\(\text{}=\sqrt{12}-\sqrt{10}\)
\(\text{}=2\sqrt{3}-\sqrt{10}\)

\(3\sqrt{15}⋅4\sqrt{3}=12\sqrt{45}=12⋅\sqrt{9}⋅\sqrt{5}=12⋅3⋅\sqrt{5}=36\sqrt{5}\)

\({8 \over 9\sqrt{5}}={8 \over 9\sqrt{5}}⋅{\sqrt{5} \over \sqrt{5}}={8\sqrt{5} \over 9⋅5}=\frac{8}{45}\sqrt{5}\text{.}\)