Wortels vereenvoudigen

\(\sqrt{\frac{1}{81}}={\sqrt{1} \over \sqrt{81}}=\frac{1}{9}\text{.}\)

\(\sqrt{1\frac{20}{49}}=\sqrt{\frac{69}{49}}={\sqrt{69} \over \sqrt{49}}={\sqrt{69} \over 7}=\frac{1}{7}\sqrt{69}\text{.}\)

\(\sqrt{1\frac{18}{31}}=\sqrt{\frac{49}{31}}={\sqrt{49} \over \sqrt{31}}={7 \over \sqrt{31}}⋅{\sqrt{31} \over \sqrt{31}}={7\sqrt{31} \over 31}=\frac{7}{31}\sqrt{31}\text{.}\)

\(\sqrt{\frac{3}{8}}={\sqrt{3} \over \sqrt{8}}⋅{\sqrt{8} \over \sqrt{8}}={\sqrt{24} \over 8}=\frac{1}{8}\sqrt{24}=\frac{1}{8}⋅2⋅\sqrt{6}=\frac{1}{4}\sqrt{6}\text{.}\)

\({8\sqrt{120} \over \sqrt{3}}=8⋅{\sqrt{120} \over \sqrt{3}}=8\sqrt{40}=8⋅\sqrt{4}⋅\sqrt{10}=8⋅2⋅\sqrt{10}=16\sqrt{10}\)

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

\(6\sqrt{28}=6⋅\sqrt{4}⋅\sqrt{7}=6⋅2⋅\sqrt{7}=12\sqrt{7}\text{.}\)

\(\sqrt{50}+\sqrt{18}=\sqrt{25}⋅\sqrt{2}+\sqrt{9}⋅\sqrt{2}=5\sqrt{2}+3\sqrt{2}\text{.}\)

\(5\sqrt{2}+3\sqrt{2}=8\sqrt{2}\text{.}\)

\(5\sqrt{20}-7\sqrt{80}=5⋅\sqrt{4}⋅\sqrt{5}-7⋅\sqrt{16}⋅\sqrt{5}\text{.}\)

\(5⋅2⋅\sqrt{5}-7⋅4⋅\sqrt{5}=10\sqrt{5}-28\sqrt{5}=-18\sqrt{5}\text{.}\)

\({4 \over 1-\sqrt{5}}={4 \over 1-\sqrt{5}}⋅{1+\sqrt{5} \over 1+\sqrt{5}}\)
\(\text{}={4(1-\sqrt{5}) \over 1-5}\)
\(\text{}=-1(1-\sqrt{5})\)
\(\text{}=-1+\sqrt{5}\)

\({4\sqrt{6} \over \sqrt{5}+\sqrt{3}}={4\sqrt{6} \over \sqrt{5}+\sqrt{3}}⋅{\sqrt{5}-\sqrt{3} \over \sqrt{5}-\sqrt{3}}\)
\(\text{}={4\sqrt{6}(\sqrt{5}-\sqrt{3}) \over 5-3}\)
\(\text{}=2\sqrt{6}(\sqrt{5}-\sqrt{3})\)
\(\text{}=2\sqrt{30}-2\sqrt{18}\)
\(\text{}=2\sqrt{30}-6\sqrt{2}\)

\(5\sqrt{6}⋅4\sqrt{10}=20\sqrt{60}=20⋅\sqrt{4}⋅\sqrt{15}=20⋅2⋅\sqrt{15}=40\sqrt{15}\)

\({9 \over 2\sqrt{7}}={9 \over 2\sqrt{7}}⋅{\sqrt{7} \over \sqrt{7}}={9\sqrt{7} \over 2⋅7}=\frac{9}{14}\sqrt{7}\text{.}\)