Rekenen met wortels (reeks 3)

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1. \(\frac{\sqrt{867}}{\sqrt{3}}\)
2. \(-\frac{\sqrt{28}}{\sqrt{7}}\)
3. \(\sqrt{10}\cdot\sqrt{490}\)
4. \(\sqrt{2}\cdot\sqrt{242}\)
5. \(-\frac{\sqrt{20}}{\sqrt{5}}\)
6. \(\frac{\sqrt{242}}{\sqrt{2}}\)
7. \(-\sqrt{6}\cdot\sqrt{726}\)
8. \(\frac{\sqrt{1575}}{\sqrt{7}}\)
9. \(\frac{\sqrt{1690}}{\sqrt{10}}\)
10. \(\frac{\sqrt{2166}}{\sqrt{6}}\)
11. \(\frac{\sqrt{176}}{\sqrt{11}}\)
12. \(\frac{\sqrt{150}}{\sqrt{6}}\)

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Verbetersleutel

1. \(\frac{\sqrt{867}}{\sqrt{3}}=\sqrt{ \frac{867}{3}}=\sqrt{ 289}=17\)
2. \(-\frac{\sqrt{28}}{\sqrt{7}}=-\sqrt{ \frac{28}{7}}=-\sqrt{ 4}=-2\)
3. \(\sqrt{10}\cdot\sqrt{490}=\sqrt{10 \cdot 490}=\sqrt{10 \cdot 10 \cdot 49}=\sqrt{10 \cdot 10} \cdot \sqrt{49}=10\cdot7=70\)
4. \(\sqrt{2}\cdot\sqrt{242}=\sqrt{2 \cdot 242}=\sqrt{2 \cdot 2 \cdot 121}=\sqrt{2 \cdot 2} \cdot \sqrt{121}=2\cdot11=22\)
5. \(-\frac{\sqrt{20}}{\sqrt{5}}=-\sqrt{ \frac{20}{5}}=-\sqrt{ 4}=-2\)
6. \(\frac{\sqrt{242}}{\sqrt{2}}=\sqrt{ \frac{242}{2}}=\sqrt{ 121}=11\)
7. \(-\sqrt{6}\cdot\sqrt{726}=-\sqrt{6 \cdot 726}=-\sqrt{6 \cdot 6 \cdot 121}=-\sqrt{6 \cdot 6} \cdot \sqrt{121}=-6\cdot11=-66\)
8. \(\frac{\sqrt{1575}}{\sqrt{7}}=\sqrt{ \frac{1575}{7}}=\sqrt{ 225}=15\)
9. \(\frac{\sqrt{1690}}{\sqrt{10}}=\sqrt{ \frac{1690}{10}}=\sqrt{ 169}=13\)
10. \(\frac{\sqrt{2166}}{\sqrt{6}}=\sqrt{ \frac{2166}{6}}=\sqrt{ 361}=19\)
11. \(\frac{\sqrt{176}}{\sqrt{11}}=\sqrt{ \frac{176}{11}}=\sqrt{ 16}=4\)
12. \(\frac{\sqrt{150}}{\sqrt{6}}=\sqrt{ \frac{150}{6}}=\sqrt{ 25}=5\)