Rekenen met wortels (reeks 3)

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1. \(\sqrt{2}\cdot\sqrt{50}\)
2. \(-\sqrt{6}\cdot\sqrt{150}\)
3. \(-\sqrt{3}\cdot\sqrt{12}\)
4. \(-\sqrt{2}\cdot\sqrt{18}\)
5. \(-\sqrt{2}\cdot\sqrt{98}\)
6. \(-\sqrt{5}\cdot\sqrt{605}\)
7. \(\sqrt{5}\cdot\sqrt{45}\)
8. \(\frac{\sqrt{605}}{\sqrt{5}}\)
9. \(-\frac{\sqrt{1859}}{\sqrt{11}}\)
10. \(\sqrt{5}\cdot\sqrt{320}\)
11. \(\sqrt{10}\cdot\sqrt{810}\)
12. \(\sqrt{2}\cdot\sqrt{162}\)

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Verbetersleutel

1. \(\sqrt{2}\cdot\sqrt{50}=\sqrt{2 \cdot 50}=\sqrt{2 \cdot 2 \cdot 25}=\sqrt{2 \cdot 2} \cdot \sqrt{25}=2\cdot5=10\)
2. \(-\sqrt{6}\cdot\sqrt{150}=-\sqrt{6 \cdot 150}=-\sqrt{6 \cdot 6 \cdot 25}=-\sqrt{6 \cdot 6} \cdot \sqrt{25}=-6\cdot5=-30\)
3. \(-\sqrt{3}\cdot\sqrt{12}=-\sqrt{3 \cdot 12}=-\sqrt{3 \cdot 3 \cdot 4}=-\sqrt{3 \cdot 3} \cdot \sqrt{4}=-3\cdot2=-6\)
4. \(-\sqrt{2}\cdot\sqrt{18}=-\sqrt{2 \cdot 18}=-\sqrt{2 \cdot 2 \cdot 9}=-\sqrt{2 \cdot 2} \cdot \sqrt{9}=-2\cdot3=-6\)
5. \(-\sqrt{2}\cdot\sqrt{98}=-\sqrt{2 \cdot 98}=-\sqrt{2 \cdot 2 \cdot 49}=-\sqrt{2 \cdot 2} \cdot \sqrt{49}=-2\cdot7=-14\)
6. \(-\sqrt{5}\cdot\sqrt{605}=-\sqrt{5 \cdot 605}=-\sqrt{5 \cdot 5 \cdot 121}=-\sqrt{5 \cdot 5} \cdot \sqrt{121}=-5\cdot11=-55\)
7. \(\sqrt{5}\cdot\sqrt{45}=\sqrt{5 \cdot 45}=\sqrt{5 \cdot 5 \cdot 9}=\sqrt{5 \cdot 5} \cdot \sqrt{9}=5\cdot3=15\)
8. \(\frac{\sqrt{605}}{\sqrt{5}}=\sqrt{ \frac{605}{5}}=\sqrt{ 121}=11\)
9. \(-\frac{\sqrt{1859}}{\sqrt{11}}=-\sqrt{ \frac{1859}{11}}=-\sqrt{ 169}=-13\)
10. \(\sqrt{5}\cdot\sqrt{320}=\sqrt{5 \cdot 320}=\sqrt{5 \cdot 5 \cdot 64}=\sqrt{5 \cdot 5} \cdot \sqrt{64}=5\cdot8=40\)
11. \(\sqrt{10}\cdot\sqrt{810}=\sqrt{10 \cdot 810}=\sqrt{10 \cdot 10 \cdot 81}=\sqrt{10 \cdot 10} \cdot \sqrt{81}=10\cdot9=90\)
12. \(\sqrt{2}\cdot\sqrt{162}=\sqrt{2 \cdot 162}=\sqrt{2 \cdot 2 \cdot 81}=\sqrt{2 \cdot 2} \cdot \sqrt{81}=2\cdot9=18\)