Rekenen met wortels (reeks 3)

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1. \(\frac{\sqrt{363}}{\sqrt{3}}\)
2. \(\frac{\sqrt{18}}{\sqrt{2}}\)
3. \(-\sqrt{2}\cdot\sqrt{162}\)
4. \(-\sqrt{10}\cdot\sqrt{490}\)
5. \(\frac{\sqrt{490}}{\sqrt{10}}\)
6. \(\sqrt{10}\cdot\sqrt{90}\)
7. \(-\frac{\sqrt{1210}}{\sqrt{10}}\)
8. \(\frac{\sqrt{810}}{\sqrt{10}}\)
9. \(-\sqrt{10}\cdot\sqrt{1210}\)
10. \(-\sqrt{6}\cdot\sqrt{726}\)
11. \(\frac{\sqrt{1690}}{\sqrt{10}}\)
12. \(-\frac{\sqrt{50}}{\sqrt{2}}\)

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Verbetersleutel

1. \(\frac{\sqrt{363}}{\sqrt{3}}=\sqrt{ \frac{363}{3}}=\sqrt{ 121}=11\)
2. \(\frac{\sqrt{18}}{\sqrt{2}}=\sqrt{ \frac{18}{2}}=\sqrt{ 9}=3\)
3. \(-\sqrt{2}\cdot\sqrt{162}=-\sqrt{2 \cdot 162}=-\sqrt{2 \cdot 2 \cdot 81}=-\sqrt{2 \cdot 2} \cdot \sqrt{81}=-2\cdot9=-18\)
4. \(-\sqrt{10}\cdot\sqrt{490}=-\sqrt{10 \cdot 490}=-\sqrt{10 \cdot 10 \cdot 49}=-\sqrt{10 \cdot 10} \cdot \sqrt{49}=-10\cdot7=-70\)
5. \(\frac{\sqrt{490}}{\sqrt{10}}=\sqrt{ \frac{490}{10}}=\sqrt{ 49}=7\)
6. \(\sqrt{10}\cdot\sqrt{90}=\sqrt{10 \cdot 90}=\sqrt{10 \cdot 10 \cdot 9}=\sqrt{10 \cdot 10} \cdot \sqrt{9}=10\cdot3=30\)
7. \(-\frac{\sqrt{1210}}{\sqrt{10}}=-\sqrt{ \frac{1210}{10}}=-\sqrt{ 121}=-11\)
8. \(\frac{\sqrt{810}}{\sqrt{10}}=\sqrt{ \frac{810}{10}}=\sqrt{ 81}=9\)
9. \(-\sqrt{10}\cdot\sqrt{1210}=-\sqrt{10 \cdot 1210}=-\sqrt{10 \cdot 10 \cdot 121}=-\sqrt{10 \cdot 10} \cdot \sqrt{121}=-10\cdot11=-110\)
10. \(-\sqrt{6}\cdot\sqrt{726}=-\sqrt{6 \cdot 726}=-\sqrt{6 \cdot 6 \cdot 121}=-\sqrt{6 \cdot 6} \cdot \sqrt{121}=-6\cdot11=-66\)
11. \(\frac{\sqrt{1690}}{\sqrt{10}}=\sqrt{ \frac{1690}{10}}=\sqrt{ 169}=13\)
12. \(-\frac{\sqrt{50}}{\sqrt{2}}=-\sqrt{ \frac{50}{2}}=-\sqrt{ 25}=-5\)