Wortels vereenvoudigen

\(\sqrt{\frac{9}{16}}={\sqrt{9} \over \sqrt{16}}=\frac{3}{4}\text{.}\)

\(\sqrt{2\frac{13}{16}}=\sqrt{\frac{45}{16}}={\sqrt{45} \over \sqrt{16}}={\sqrt{45} \over 4}=\frac{1}{4}\sqrt{45}=\frac{1}{4}⋅3⋅\sqrt{5}=\frac{3}{4}\sqrt{5}\text{.}\)

\(\sqrt{\frac{49}{59}}={\sqrt{49} \over \sqrt{59}}={7 \over \sqrt{59}}⋅{\sqrt{59} \over \sqrt{59}}={7\sqrt{59} \over 59}=\frac{7}{59}\sqrt{59}\text{.}\)

\(\sqrt{22\frac{1}{2}}=\sqrt{\frac{45}{2}}={\sqrt{45} \over \sqrt{2}}⋅{\sqrt{2} \over \sqrt{2}}={\sqrt{90} \over 2}=\frac{1}{2}\sqrt{90}=\frac{1}{2}⋅3⋅\sqrt{10}=1\frac{1}{2}\sqrt{10}\text{.}\)

\({14\sqrt{200} \over 7\sqrt{10}}={14 \over 7}⋅{\sqrt{200} \over \sqrt{10}}=2\sqrt{20}=2⋅\sqrt{4}⋅\sqrt{5}=2⋅2⋅\sqrt{5}=4\sqrt{5}\)

\(\sqrt{75}=\sqrt{25}⋅\sqrt{3}=5\sqrt{3}\text{.}\)

\(-4\sqrt{700}=-4⋅\sqrt{100}⋅\sqrt{7}=-4⋅10⋅\sqrt{7}=-40\sqrt{7}\text{.}\)

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

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

\(2\sqrt{80}-5\sqrt{20}=2⋅\sqrt{16}⋅\sqrt{5}-5⋅\sqrt{4}⋅\sqrt{5}\text{.}\)

\(2⋅4⋅\sqrt{5}-5⋅2⋅\sqrt{5}=8\sqrt{5}-10\sqrt{5}=-2\sqrt{5}\text{.}\)

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

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

\(3\sqrt{3}⋅5\sqrt{6}=15\sqrt{18}=15⋅\sqrt{9}⋅\sqrt{2}=15⋅3⋅\sqrt{2}=45\sqrt{2}\)

\({4 \over 3\sqrt{5}}={4 \over 3\sqrt{5}}⋅{\sqrt{5} \over \sqrt{5}}={4\sqrt{5} \over 3⋅5}=\frac{4}{15}\sqrt{5}\text{.}\)