Wortels vereenvoudigen

\(\sqrt{\frac{4}{25}}={\sqrt{4} \over \sqrt{25}}=\frac{2}{5}\text{.}\)

\(\sqrt{\frac{11}{16}}={\sqrt{11} \over \sqrt{16}}={\sqrt{11} \over 4}=\frac{1}{4}\sqrt{11}\text{.}\)

\(\sqrt{2\frac{6}{29}}=\sqrt{\frac{64}{29}}={\sqrt{64} \over \sqrt{29}}={8 \over \sqrt{29}}⋅{\sqrt{29} \over \sqrt{29}}={8\sqrt{29} \over 29}=\frac{8}{29}\sqrt{29}\text{.}\)

\(\sqrt{9\frac{3}{8}}=\sqrt{\frac{75}{8}}={\sqrt{75} \over \sqrt{8}}⋅{\sqrt{8} \over \sqrt{8}}={\sqrt{600} \over 8}=\frac{1}{8}\sqrt{600}=\frac{1}{8}⋅10⋅\sqrt{6}=1\frac{1}{4}\sqrt{6}\text{.}\)

\({12\sqrt{168} \over 4\sqrt{7}}={12 \over 4}⋅{\sqrt{168} \over \sqrt{7}}=3\sqrt{24}=3⋅\sqrt{4}⋅\sqrt{6}=3⋅2⋅\sqrt{6}=6\sqrt{6}\)

\(\sqrt{500}=\sqrt{100}⋅\sqrt{5}=10\sqrt{5}\text{.}\)

\(-5\sqrt{32}=-5⋅\sqrt{16}⋅\sqrt{2}=-5⋅4⋅\sqrt{2}=-20\sqrt{2}\text{.}\)

\(\sqrt{45}+\sqrt{125}=\sqrt{9}⋅\sqrt{5}+\sqrt{25}⋅\sqrt{5}=3\sqrt{5}+5\sqrt{5}\text{.}\)

\(3\sqrt{5}+5\sqrt{5}=8\sqrt{5}\text{.}\)

\(4\sqrt{32}+6\sqrt{18}=4⋅\sqrt{16}⋅\sqrt{2}+6⋅\sqrt{9}⋅\sqrt{2}\text{.}\)

\(4⋅4⋅\sqrt{2}+6⋅3⋅\sqrt{2}=16\sqrt{2}+18\sqrt{2}=34\sqrt{2}\text{.}\)

\({3 \over 6+\sqrt{2}}={3 \over 6+\sqrt{2}}⋅{6-\sqrt{2} \over 6-\sqrt{2}}\)
\(\text{}={3(6+\sqrt{2}) \over 36-2}\)
\(\text{}=\frac{3}{34}(6+\sqrt{2})\)
\(\text{}=\frac{9}{17}+\frac{3}{34}\sqrt{2}\)

\({4\sqrt{6} \over \sqrt{3}+\sqrt{2}}={4\sqrt{6} \over \sqrt{3}+\sqrt{2}}⋅{\sqrt{3}-\sqrt{2} \over \sqrt{3}-\sqrt{2}}\)
\(\text{}={4\sqrt{6}(\sqrt{3}-\sqrt{2}) \over 3-2}\)
\(\text{}=4\sqrt{6}(\sqrt{3}-\sqrt{2})\)
\(\text{}=4\sqrt{18}-4\sqrt{12}\)
\(\text{}=12\sqrt{2}-8\sqrt{3}\)

\(4\sqrt{6}⋅2\sqrt{10}=8\sqrt{60}=8⋅\sqrt{4}⋅\sqrt{15}=8⋅2⋅\sqrt{15}=16\sqrt{15}\)

\({4 \over 5\sqrt{7}}={4 \over 5\sqrt{7}}⋅{\sqrt{7} \over \sqrt{7}}={4\sqrt{7} \over 5⋅7}=\frac{4}{35}\sqrt{7}\text{.}\)