Rekenen met wortels (reeks 3)

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1. \(\sqrt{10}\cdot\sqrt{490}\)
2. \(\sqrt{3}\cdot\sqrt{147}\)
3. \(-\sqrt{5}\cdot\sqrt{45}\)
4. \(\sqrt{6}\cdot\sqrt{294}\)
5. \(-\frac{\sqrt{2890}}{\sqrt{10}}\)
6. \(\frac{\sqrt{490}}{\sqrt{10}}\)
7. \(-\frac{\sqrt{98}}{\sqrt{2}}\)
8. \(-\frac{\sqrt{63}}{\sqrt{7}}\)
9. \(-\frac{\sqrt{1584}}{\sqrt{11}}\)
10. \(\sqrt{5}\cdot\sqrt{20}\)
11. \(\frac{\sqrt{567}}{\sqrt{7}}\)
12. \(-\frac{\sqrt{150}}{\sqrt{6}}\)

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Verbetersleutel

1. \(\sqrt{10}\cdot\sqrt{490}=\sqrt{10 \cdot 490}=\sqrt{10 \cdot 10 \cdot 49}=\sqrt{10 \cdot 10} \cdot \sqrt{49}=10\cdot7=70\)
2. \(\sqrt{3}\cdot\sqrt{147}=\sqrt{3 \cdot 147}=\sqrt{3 \cdot 3 \cdot 49}=\sqrt{3 \cdot 3} \cdot \sqrt{49}=3\cdot7=21\)
3. \(-\sqrt{5}\cdot\sqrt{45}=-\sqrt{5 \cdot 45}=-\sqrt{5 \cdot 5 \cdot 9}=-\sqrt{5 \cdot 5} \cdot \sqrt{9}=-5\cdot3=-15\)
4. \(\sqrt{6}\cdot\sqrt{294}=\sqrt{6 \cdot 294}=\sqrt{6 \cdot 6 \cdot 49}=\sqrt{6 \cdot 6} \cdot \sqrt{49}=6\cdot7=42\)
5. \(-\frac{\sqrt{2890}}{\sqrt{10}}=-\sqrt{ \frac{2890}{10}}=-\sqrt{ 289}=-17\)
6. \(\frac{\sqrt{490}}{\sqrt{10}}=\sqrt{ \frac{490}{10}}=\sqrt{ 49}=7\)
7. \(-\frac{\sqrt{98}}{\sqrt{2}}=-\sqrt{ \frac{98}{2}}=-\sqrt{ 49}=-7\)
8. \(-\frac{\sqrt{63}}{\sqrt{7}}=-\sqrt{ \frac{63}{7}}=-\sqrt{ 9}=-3\)
9. \(-\frac{\sqrt{1584}}{\sqrt{11}}=-\sqrt{ \frac{1584}{11}}=-\sqrt{ 144}=-12\)
10. \(\sqrt{5}\cdot\sqrt{20}=\sqrt{5 \cdot 20}=\sqrt{5 \cdot 5 \cdot 4}=\sqrt{5 \cdot 5} \cdot \sqrt{4}=5\cdot2=10\)
11. \(\frac{\sqrt{567}}{\sqrt{7}}=\sqrt{ \frac{567}{7}}=\sqrt{ 81}=9\)
12. \(-\frac{\sqrt{150}}{\sqrt{6}}=-\sqrt{ \frac{150}{6}}=-\sqrt{ 25}=-5\)