Wortels vereenvoudigen

\(\sqrt{\frac{1}{36}}={\sqrt{1} \over \sqrt{36}}=\frac{1}{6}\text{.}\)

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

\(\sqrt{6\frac{1}{8}}=\sqrt{\frac{49}{8}}={\sqrt{49} \over \sqrt{8}}={7 \over \sqrt{8}}⋅{\sqrt{8} \over \sqrt{8}}={7\sqrt{8} \over 8}=\frac{7}{8}\sqrt{8}=\frac{7}{8}⋅2⋅\sqrt{2}=1\frac{3}{4}\sqrt{2}\text{.}\)

\(\sqrt{8\frac{1}{2}}=\sqrt{\frac{17}{2}}={\sqrt{17} \over \sqrt{2}}⋅{\sqrt{2} \over \sqrt{2}}={\sqrt{34} \over 2}=\frac{1}{2}\sqrt{34}\text{.}\)

\({35\sqrt{96} \over 7\sqrt{8}}={35 \over 7}⋅{\sqrt{96} \over \sqrt{8}}=5\sqrt{12}=5⋅\sqrt{4}⋅\sqrt{3}=5⋅2⋅\sqrt{3}=10\sqrt{3}\)

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

\(6\sqrt{20}=6⋅\sqrt{4}⋅\sqrt{5}=6⋅2⋅\sqrt{5}=12\sqrt{5}\text{.}\)

\(\sqrt{18}+\sqrt{200}=\sqrt{9}⋅\sqrt{2}+\sqrt{100}⋅\sqrt{2}=3\sqrt{2}+10\sqrt{2}\text{.}\)

\(3\sqrt{2}+10\sqrt{2}=13\sqrt{2}\text{.}\)

\(7\sqrt{12}+3\sqrt{27}=7⋅\sqrt{4}⋅\sqrt{3}+3⋅\sqrt{9}⋅\sqrt{3}\text{.}\)

\(7⋅2⋅\sqrt{3}+3⋅3⋅\sqrt{3}=14\sqrt{3}+9\sqrt{3}=23\sqrt{3}\text{.}\)

\({3 \over 5+\sqrt{2}}={3 \over 5+\sqrt{2}}⋅{5-\sqrt{2} \over 5-\sqrt{2}}\)
\(\text{}={3(5+\sqrt{2}) \over 25-2}\)
\(\text{}=\frac{3}{23}(5+\sqrt{2})\)
\(\text{}=\frac{15}{23}+\frac{3}{23}\sqrt{2}\)

\({2\sqrt{5} \over \sqrt{3}+\sqrt{6}}={2\sqrt{5} \over \sqrt{3}+\sqrt{6}}⋅{\sqrt{3}-\sqrt{6} \over \sqrt{3}-\sqrt{6}}\)
\(\text{}={2\sqrt{5}(\sqrt{3}-\sqrt{6}) \over 3-6}\)
\(\text{}=-\frac{2}{3}\sqrt{5}(\sqrt{3}-\sqrt{6})\)
\(\text{}=-\frac{2}{3}\sqrt{15}+\frac{2}{3}\sqrt{30}\)

\(4\sqrt{6}⋅5\sqrt{2}=20\sqrt{12}=20⋅\sqrt{4}⋅\sqrt{3}=20⋅2⋅\sqrt{3}=40\sqrt{3}\)

\({5 \over 3\sqrt{2}}={5 \over 3\sqrt{2}}⋅{\sqrt{2} \over \sqrt{2}}={5\sqrt{2} \over 3⋅2}=\frac{5}{6}\sqrt{2}\text{.}\)