Rekenen met wortels (reeks 3)

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1. \(\sqrt{2}\cdot\sqrt{162}\)
2. \(\frac{\sqrt{768}}{\sqrt{3}}\)
3. \(-\frac{\sqrt{90}}{\sqrt{10}}\)
4. \(\frac{\sqrt{1280}}{\sqrt{5}}\)
5. \(-\frac{\sqrt{2890}}{\sqrt{10}}\)
6. \(-\sqrt{6}\cdot\sqrt{726}\)
7. \(-\frac{\sqrt{847}}{\sqrt{7}}\)
8. \(-\sqrt{3}\cdot\sqrt{48}\)
9. \(\frac{\sqrt{2548}}{\sqrt{13}}\)
10. \(-\frac{\sqrt{1734}}{\sqrt{6}}\)
11. \(\frac{\sqrt{3610}}{\sqrt{10}}\)
12. \(\frac{\sqrt{405}}{\sqrt{5}}\)

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Verbetersleutel

1. \(\sqrt{2}\cdot\sqrt{162}=\sqrt{2 \cdot 162}=\sqrt{2 \cdot 2 \cdot 81}=\sqrt{2 \cdot 2} \cdot \sqrt{81}=2\cdot9=18\)
2. \(\frac{\sqrt{768}}{\sqrt{3}}=\sqrt{ \frac{768}{3}}=\sqrt{ 256}=16\)
3. \(-\frac{\sqrt{90}}{\sqrt{10}}=-\sqrt{ \frac{90}{10}}=-\sqrt{ 9}=-3\)
4. \(\frac{\sqrt{1280}}{\sqrt{5}}=\sqrt{ \frac{1280}{5}}=\sqrt{ 256}=16\)
5. \(-\frac{\sqrt{2890}}{\sqrt{10}}=-\sqrt{ \frac{2890}{10}}=-\sqrt{ 289}=-17\)
6. \(-\sqrt{6}\cdot\sqrt{726}=-\sqrt{6 \cdot 726}=-\sqrt{6 \cdot 6 \cdot 121}=-\sqrt{6 \cdot 6} \cdot \sqrt{121}=-6\cdot11=-66\)
7. \(-\frac{\sqrt{847}}{\sqrt{7}}=-\sqrt{ \frac{847}{7}}=-\sqrt{ 121}=-11\)
8. \(-\sqrt{3}\cdot\sqrt{48}=-\sqrt{3 \cdot 48}=-\sqrt{3 \cdot 3 \cdot 16}=-\sqrt{3 \cdot 3} \cdot \sqrt{16}=-3\cdot4=-12\)
9. \(\frac{\sqrt{2548}}{\sqrt{13}}=\sqrt{ \frac{2548}{13}}=\sqrt{ 196}=14\)
10. \(-\frac{\sqrt{1734}}{\sqrt{6}}=-\sqrt{ \frac{1734}{6}}=-\sqrt{ 289}=-17\)
11. \(\frac{\sqrt{3610}}{\sqrt{10}}=\sqrt{ \frac{3610}{10}}=\sqrt{ 361}=19\)
12. \(\frac{\sqrt{405}}{\sqrt{5}}=\sqrt{ \frac{405}{5}}=\sqrt{ 81}=9\)