Rekenen met wortels (reeks 3)

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1. \(-\sqrt{2}\cdot\sqrt{162}\)
2. \(\sqrt{3}\cdot\sqrt{12}\)
3. \(-\frac{\sqrt{90}}{\sqrt{10}}\)
4. \(-\frac{\sqrt{1183}}{\sqrt{7}}\)
5. \(\frac{\sqrt{363}}{\sqrt{3}}\)
6. \(\frac{\sqrt{980}}{\sqrt{5}}\)
7. \(\frac{\sqrt{567}}{\sqrt{7}}\)
8. \(-\sqrt{2}\cdot\sqrt{98}\)
9. \(-\sqrt{2}\cdot\sqrt{242}\)
10. \(-\frac{\sqrt{2527}}{\sqrt{7}}\)
11. \(-\sqrt{5}\cdot\sqrt{80}\)
12. \(-\sqrt{2}\cdot\sqrt{18}\)

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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. \(\sqrt{3}\cdot\sqrt{12}=\sqrt{3 \cdot 12}=\sqrt{3 \cdot 3 \cdot 4}=\sqrt{3 \cdot 3} \cdot \sqrt{4}=3\cdot2=6\)
3. \(-\frac{\sqrt{90}}{\sqrt{10}}=-\sqrt{ \frac{90}{10}}=-\sqrt{ 9}=-3\)
4. \(-\frac{\sqrt{1183}}{\sqrt{7}}=-\sqrt{ \frac{1183}{7}}=-\sqrt{ 169}=-13\)
5. \(\frac{\sqrt{363}}{\sqrt{3}}=\sqrt{ \frac{363}{3}}=\sqrt{ 121}=11\)
6. \(\frac{\sqrt{980}}{\sqrt{5}}=\sqrt{ \frac{980}{5}}=\sqrt{ 196}=14\)
7. \(\frac{\sqrt{567}}{\sqrt{7}}=\sqrt{ \frac{567}{7}}=\sqrt{ 81}=9\)
8. \(-\sqrt{2}\cdot\sqrt{98}=-\sqrt{2 \cdot 98}=-\sqrt{2 \cdot 2 \cdot 49}=-\sqrt{2 \cdot 2} \cdot \sqrt{49}=-2\cdot7=-14\)
9. \(-\sqrt{2}\cdot\sqrt{242}=-\sqrt{2 \cdot 242}=-\sqrt{2 \cdot 2 \cdot 121}=-\sqrt{2 \cdot 2} \cdot \sqrt{121}=-2\cdot11=-22\)
10. \(-\frac{\sqrt{2527}}{\sqrt{7}}=-\sqrt{ \frac{2527}{7}}=-\sqrt{ 361}=-19\)
11. \(-\sqrt{5}\cdot\sqrt{80}=-\sqrt{5 \cdot 80}=-\sqrt{5 \cdot 5 \cdot 16}=-\sqrt{5 \cdot 5} \cdot \sqrt{16}=-5\cdot4=-20\)
12. \(-\sqrt{2}\cdot\sqrt{18}=-\sqrt{2 \cdot 18}=-\sqrt{2 \cdot 2 \cdot 9}=-\sqrt{2 \cdot 2} \cdot \sqrt{9}=-2\cdot3=-6\)