Rekenen met wortels (reeks 3)

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1. \(\frac{\sqrt{845}}{\sqrt{5}}\)
2. \(-\sqrt{5}\cdot\sqrt{405}\)
3. \(-\sqrt{2}\cdot\sqrt{162}\)
4. \(-\frac{\sqrt{320}}{\sqrt{5}}\)
5. \(-\frac{\sqrt{1734}}{\sqrt{6}}\)
6. \(-\frac{\sqrt{162}}{\sqrt{2}}\)
7. \(-\sqrt{6}\cdot\sqrt{150}\)
8. \(\frac{\sqrt{28}}{\sqrt{7}}\)
9. \(\frac{\sqrt{192}}{\sqrt{3}}\)
10. \(\frac{\sqrt{150}}{\sqrt{6}}\)
11. \(-\frac{\sqrt{75}}{\sqrt{3}}\)
12. \(-\sqrt{3}\cdot\sqrt{147}\)

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Verbetersleutel

1. \(\frac{\sqrt{845}}{\sqrt{5}}=\sqrt{ \frac{845}{5}}=\sqrt{ 169}=13\)
2. \(-\sqrt{5}\cdot\sqrt{405}=-\sqrt{5 \cdot 405}=-\sqrt{5 \cdot 5 \cdot 81}=-\sqrt{5 \cdot 5} \cdot \sqrt{81}=-5\cdot9=-45\)
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. \(-\frac{\sqrt{320}}{\sqrt{5}}=-\sqrt{ \frac{320}{5}}=-\sqrt{ 64}=-8\)
5. \(-\frac{\sqrt{1734}}{\sqrt{6}}=-\sqrt{ \frac{1734}{6}}=-\sqrt{ 289}=-17\)
6. \(-\frac{\sqrt{162}}{\sqrt{2}}=-\sqrt{ \frac{162}{2}}=-\sqrt{ 81}=-9\)
7. \(-\sqrt{6}\cdot\sqrt{150}=-\sqrt{6 \cdot 150}=-\sqrt{6 \cdot 6 \cdot 25}=-\sqrt{6 \cdot 6} \cdot \sqrt{25}=-6\cdot5=-30\)
8. \(\frac{\sqrt{28}}{\sqrt{7}}=\sqrt{ \frac{28}{7}}=\sqrt{ 4}=2\)
9. \(\frac{\sqrt{192}}{\sqrt{3}}=\sqrt{ \frac{192}{3}}=\sqrt{ 64}=8\)
10. \(\frac{\sqrt{150}}{\sqrt{6}}=\sqrt{ \frac{150}{6}}=\sqrt{ 25}=5\)
11. \(-\frac{\sqrt{75}}{\sqrt{3}}=-\sqrt{ \frac{75}{3}}=-\sqrt{ 25}=-5\)
12. \(-\sqrt{3}\cdot\sqrt{147}=-\sqrt{3 \cdot 147}=-\sqrt{3 \cdot 3 \cdot 49}=-\sqrt{3 \cdot 3} \cdot \sqrt{49}=-3\cdot7=-21\)