Rekenen met wortels (reeks 3)

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1. \(\frac{\sqrt{578}}{\sqrt{2}}\)
2. \(-\sqrt{2}\cdot\sqrt{242}\)
3. \(\sqrt{10}\cdot\sqrt{90}\)
4. \(-\frac{\sqrt{4693}}{\sqrt{13}}\)
5. \(\frac{\sqrt{3610}}{\sqrt{10}}\)
6. \(\sqrt{3}\cdot\sqrt{75}\)
7. \(-\frac{\sqrt{704}}{\sqrt{11}}\)
8. \(-\frac{\sqrt{1573}}{\sqrt{13}}\)
9. \(-\frac{\sqrt{726}}{\sqrt{6}}\)
10. \(-\sqrt{2}\cdot\sqrt{50}\)
11. \(\frac{\sqrt{2890}}{\sqrt{10}}\)
12. \(-\frac{\sqrt{768}}{\sqrt{3}}\)

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Verbetersleutel

1. \(\frac{\sqrt{578}}{\sqrt{2}}=\sqrt{ \frac{578}{2}}=\sqrt{ 289}=17\)
2. \(-\sqrt{2}\cdot\sqrt{242}=-\sqrt{2 \cdot 242}=-\sqrt{2 \cdot 2 \cdot 121}=-\sqrt{2 \cdot 2} \cdot \sqrt{121}=-2\cdot11=-22\)
3. \(\sqrt{10}\cdot\sqrt{90}=\sqrt{10 \cdot 90}=\sqrt{10 \cdot 10 \cdot 9}=\sqrt{10 \cdot 10} \cdot \sqrt{9}=10\cdot3=30\)
4. \(-\frac{\sqrt{4693}}{\sqrt{13}}=-\sqrt{ \frac{4693}{13}}=-\sqrt{ 361}=-19\)
5. \(\frac{\sqrt{3610}}{\sqrt{10}}=\sqrt{ \frac{3610}{10}}=\sqrt{ 361}=19\)
6. \(\sqrt{3}\cdot\sqrt{75}=\sqrt{3 \cdot 75}=\sqrt{3 \cdot 3 \cdot 25}=\sqrt{3 \cdot 3} \cdot \sqrt{25}=3\cdot5=15\)
7. \(-\frac{\sqrt{704}}{\sqrt{11}}=-\sqrt{ \frac{704}{11}}=-\sqrt{ 64}=-8\)
8. \(-\frac{\sqrt{1573}}{\sqrt{13}}=-\sqrt{ \frac{1573}{13}}=-\sqrt{ 121}=-11\)
9. \(-\frac{\sqrt{726}}{\sqrt{6}}=-\sqrt{ \frac{726}{6}}=-\sqrt{ 121}=-11\)
10. \(-\sqrt{2}\cdot\sqrt{50}=-\sqrt{2 \cdot 50}=-\sqrt{2 \cdot 2 \cdot 25}=-\sqrt{2 \cdot 2} \cdot \sqrt{25}=-2\cdot5=-10\)
11. \(\frac{\sqrt{2890}}{\sqrt{10}}=\sqrt{ \frac{2890}{10}}=\sqrt{ 289}=17\)
12. \(-\frac{\sqrt{768}}{\sqrt{3}}=-\sqrt{ \frac{768}{3}}=-\sqrt{ 256}=-16\)