Wortels vereenvoudigen

a

\(\sqrt{3\frac{6}{25}}=\sqrt{\frac{81}{25}}={\sqrt{81} \over \sqrt{25}}=\frac{9}{5}=1\frac{4}{5}\text{.}\)

1p

a

\(\sqrt{\frac{10}{81}}={\sqrt{10} \over \sqrt{81}}={\sqrt{10} \over 9}=\frac{1}{9}\sqrt{10}\text{.}\)

1p

a

\(\sqrt{\frac{9}{40}}={\sqrt{9} \over \sqrt{40}}={3 \over \sqrt{40}}⋅{\sqrt{40} \over \sqrt{40}}={3\sqrt{40} \over 40}=\frac{3}{40}\sqrt{40}=\frac{3}{40}⋅2⋅\sqrt{10}=\frac{3}{20}\sqrt{10}\text{.}\)

1p

a

\(\sqrt{10\frac{2}{3}}=\sqrt{\frac{32}{3}}={\sqrt{32} \over \sqrt{3}}⋅{\sqrt{3} \over \sqrt{3}}={\sqrt{96} \over 3}=\frac{1}{3}\sqrt{96}=\frac{1}{3}⋅4⋅\sqrt{6}=1\frac{1}{3}\sqrt{6}\text{.}\)

1p

a

\({21\sqrt{196} \over 7\sqrt{7}}={21 \over 7}⋅{\sqrt{196} \over \sqrt{7}}=3\sqrt{28}=3⋅\sqrt{4}⋅\sqrt{7}=3⋅2⋅\sqrt{7}=6\sqrt{7}\)

1p

a

\(\sqrt{125}=\sqrt{25}⋅\sqrt{5}=5\sqrt{5}\text{.}\)

1p

a

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

1p

a

\(\sqrt{27}+\sqrt{75}=\sqrt{9}⋅\sqrt{3}+\sqrt{25}⋅\sqrt{3}=3\sqrt{3}+5\sqrt{3}\text{.}\)

1p

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

1p

a

\(5\sqrt{125}-7\sqrt{500}=5⋅\sqrt{25}⋅\sqrt{5}-7⋅\sqrt{100}⋅\sqrt{5}\text{.}\)

1p

\(5⋅5⋅\sqrt{5}-7⋅10⋅\sqrt{5}=25\sqrt{5}-70\sqrt{5}=-45\sqrt{5}\text{.}\)

1p

a

\(3\sqrt{14}⋅2\sqrt{7}=6\sqrt{98}=6⋅\sqrt{49}⋅\sqrt{2}=6⋅7⋅\sqrt{2}=42\sqrt{2}\)

1p

a

\({5 \over 7\sqrt{7}}={5 \over 7\sqrt{7}}⋅{\sqrt{7} \over \sqrt{7}}={5\sqrt{7} \over 7⋅7}=\frac{5}{49}\sqrt{7}\text{.}\)

1p