Wortels vereenvoudigen

\(\sqrt{20\frac{1}{4}}=\sqrt{\frac{81}{4}}={\sqrt{81} \over \sqrt{4}}=\frac{9}{2}=4\frac{1}{2}\text{.}\)

\(\sqrt{2\frac{5}{16}}=\sqrt{\frac{37}{16}}={\sqrt{37} \over \sqrt{16}}={\sqrt{37} \over 4}=\frac{1}{4}\sqrt{37}\text{.}\)

\(\sqrt{\frac{4}{99}}={\sqrt{4} \over \sqrt{99}}={2 \over \sqrt{99}}⋅{\sqrt{99} \over \sqrt{99}}={2\sqrt{99} \over 99}=\frac{2}{99}\sqrt{99}=\frac{2}{99}⋅3⋅\sqrt{11}=\frac{2}{33}\sqrt{11}\text{.}\)

\(\sqrt{\frac{3}{20}}={\sqrt{3} \over \sqrt{20}}⋅{\sqrt{20} \over \sqrt{20}}={\sqrt{60} \over 20}=\frac{1}{20}\sqrt{60}=\frac{1}{20}⋅2⋅\sqrt{15}=\frac{1}{10}\sqrt{15}\text{.}\)

\({28\sqrt{48} \over 7\sqrt{6}}={28 \over 7}⋅{\sqrt{48} \over \sqrt{6}}=4\sqrt{8}=4⋅\sqrt{4}⋅\sqrt{2}=4⋅2⋅\sqrt{2}=8\sqrt{2}\)

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

\(3\sqrt{48}=3⋅\sqrt{16}⋅\sqrt{3}=3⋅4⋅\sqrt{3}=12\sqrt{3}\text{.}\)

\(\sqrt{48}+\sqrt{27}=\sqrt{16}⋅\sqrt{3}+\sqrt{9}⋅\sqrt{3}=4\sqrt{3}+3\sqrt{3}\text{.}\)

\(4\sqrt{3}+3\sqrt{3}=7\sqrt{3}\text{.}\)

\(7\sqrt{27}-2\sqrt{75}=7⋅\sqrt{9}⋅\sqrt{3}-2⋅\sqrt{25}⋅\sqrt{3}\text{.}\)

\(7⋅3⋅\sqrt{3}-2⋅5⋅\sqrt{3}=21\sqrt{3}-10\sqrt{3}=11\sqrt{3}\text{.}\)

\({-2 \over 4-\sqrt{6}}={-2 \over 4-\sqrt{6}}⋅{4+\sqrt{6} \over 4+\sqrt{6}}\)
\(\text{}={-2(4-\sqrt{6}) \over 16-6}\)
\(\text{}=-\frac{1}{5}(4-\sqrt{6})\)
\(\text{}=-\frac{4}{5}+\frac{1}{5}\sqrt{6}\)

\({4\sqrt{5} \over \sqrt{3}-\sqrt{2}}={4\sqrt{5} \over \sqrt{3}-\sqrt{2}}⋅{\sqrt{3}+\sqrt{2} \over \sqrt{3}+\sqrt{2}}\)
\(\text{}={4\sqrt{5}(\sqrt{3}+\sqrt{2}) \over 3-2}\)
\(\text{}=4\sqrt{5}(\sqrt{3}+\sqrt{2})\)
\(\text{}=4\sqrt{15}+4\sqrt{10}\)

\(3\sqrt{6}⋅4\sqrt{14}=12\sqrt{84}=12⋅\sqrt{4}⋅\sqrt{21}=12⋅2⋅\sqrt{21}=24\sqrt{21}\)

\({3 \over 5\sqrt{7}}={3 \over 5\sqrt{7}}⋅{\sqrt{7} \over \sqrt{7}}={3\sqrt{7} \over 5⋅7}=\frac{3}{35}\sqrt{7}\text{.}\)