Rekenen met wortels (reeks 3)

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1. \(-\sqrt{3}\cdot\sqrt{363}\)
2. \(\frac{\sqrt{2166}}{\sqrt{6}}\)
3. \(\frac{\sqrt{1100}}{\sqrt{11}}\)
4. \(\frac{\sqrt{726}}{\sqrt{6}}\)
5. \(\frac{\sqrt{588}}{\sqrt{3}}\)
6. \(-\frac{\sqrt{300}}{\sqrt{3}}\)
7. \(\sqrt{2}\cdot\sqrt{18}\)
8. \(\frac{\sqrt{20}}{\sqrt{5}}\)
9. \(-\sqrt{5}\cdot\sqrt{245}\)
10. \(-\frac{\sqrt{1573}}{\sqrt{13}}\)
11. \(\sqrt{10}\cdot\sqrt{490}\)
12. \(\frac{\sqrt{2548}}{\sqrt{13}}\)

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Verbetersleutel

1. \(-\sqrt{3}\cdot\sqrt{363}=-\sqrt{3 \cdot 363}=-\sqrt{3 \cdot 3 \cdot 121}=-\sqrt{3 \cdot 3} \cdot \sqrt{121}=-3\cdot11=-33\)
2. \(\frac{\sqrt{2166}}{\sqrt{6}}=\sqrt{ \frac{2166}{6}}=\sqrt{ 361}=19\)
3. \(\frac{\sqrt{1100}}{\sqrt{11}}=\sqrt{ \frac{1100}{11}}=\sqrt{ 100}=10\)
4. \(\frac{\sqrt{726}}{\sqrt{6}}=\sqrt{ \frac{726}{6}}=\sqrt{ 121}=11\)
5. \(\frac{\sqrt{588}}{\sqrt{3}}=\sqrt{ \frac{588}{3}}=\sqrt{ 196}=14\)
6. \(-\frac{\sqrt{300}}{\sqrt{3}}=-\sqrt{ \frac{300}{3}}=-\sqrt{ 100}=-10\)
7. \(\sqrt{2}\cdot\sqrt{18}=\sqrt{2 \cdot 18}=\sqrt{2 \cdot 2 \cdot 9}=\sqrt{2 \cdot 2} \cdot \sqrt{9}=2\cdot3=6\)
8. \(\frac{\sqrt{20}}{\sqrt{5}}=\sqrt{ \frac{20}{5}}=\sqrt{ 4}=2\)
9. \(-\sqrt{5}\cdot\sqrt{245}=-\sqrt{5 \cdot 245}=-\sqrt{5 \cdot 5 \cdot 49}=-\sqrt{5 \cdot 5} \cdot \sqrt{49}=-5\cdot7=-35\)
10. \(-\frac{\sqrt{1573}}{\sqrt{13}}=-\sqrt{ \frac{1573}{13}}=-\sqrt{ 121}=-11\)
11. \(\sqrt{10}\cdot\sqrt{490}=\sqrt{10 \cdot 490}=\sqrt{10 \cdot 10 \cdot 49}=\sqrt{10 \cdot 10} \cdot \sqrt{49}=10\cdot7=70\)
12. \(\frac{\sqrt{2548}}{\sqrt{13}}=\sqrt{ \frac{2548}{13}}=\sqrt{ 196}=14\)