Wortels vereenvoudigen

\(\sqrt{1\frac{15}{49}}=\sqrt{\frac{64}{49}}={\sqrt{64} \over \sqrt{49}}=\frac{8}{7}=1\frac{1}{7}\text{.}\)

\(\sqrt{\frac{62}{81}}={\sqrt{62} \over \sqrt{81}}={\sqrt{62} \over 9}=\frac{1}{9}\sqrt{62}\text{.}\)

\(\sqrt{\frac{25}{63}}={\sqrt{25} \over \sqrt{63}}={5 \over \sqrt{63}}⋅{\sqrt{63} \over \sqrt{63}}={5\sqrt{63} \over 63}=\frac{5}{63}\sqrt{63}=\frac{5}{63}⋅3⋅\sqrt{7}=\frac{5}{21}\sqrt{7}\text{.}\)

\(\sqrt{1\frac{1}{7}}=\sqrt{\frac{8}{7}}={\sqrt{8} \over \sqrt{7}}⋅{\sqrt{7} \over \sqrt{7}}={\sqrt{56} \over 7}=\frac{1}{7}\sqrt{56}=\frac{1}{7}⋅2⋅\sqrt{14}=\frac{2}{7}\sqrt{14}\text{.}\)

\({12\sqrt{56} \over 4\sqrt{7}}={12 \over 4}⋅{\sqrt{56} \over \sqrt{7}}=3\sqrt{8}=3⋅\sqrt{4}⋅\sqrt{2}=3⋅2⋅\sqrt{2}=6\sqrt{2}\)

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

\(6\sqrt{175}=6⋅\sqrt{25}⋅\sqrt{7}=6⋅5⋅\sqrt{7}=30\sqrt{7}\text{.}\)

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

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

\(4\sqrt{200}+5\sqrt{32}=4⋅\sqrt{100}⋅\sqrt{2}+5⋅\sqrt{16}⋅\sqrt{2}\text{.}\)

\(4⋅10⋅\sqrt{2}+5⋅4⋅\sqrt{2}=40\sqrt{2}+20\sqrt{2}=60\sqrt{2}\text{.}\)

\(3\sqrt{5}⋅4\sqrt{15}=12\sqrt{75}=12⋅\sqrt{25}⋅\sqrt{3}=12⋅5⋅\sqrt{3}=60\sqrt{3}\)

\({9 \over 4\sqrt{5}}={9 \over 4\sqrt{5}}⋅{\sqrt{5} \over \sqrt{5}}={9\sqrt{5} \over 4⋅5}=\frac{9}{20}\sqrt{5}\text{.}\)