Rekenen met wortels (reeks 3)

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1. \(\frac{\sqrt{18}}{\sqrt{2}}\)
2. \(\sqrt{3}\cdot\sqrt{12}\)
3. \(-\frac{\sqrt{726}}{\sqrt{6}}\)
4. \(-\frac{\sqrt{2890}}{\sqrt{10}}\)
5. \(\frac{\sqrt{90}}{\sqrt{10}}\)
6. \(-\sqrt{6}\cdot\sqrt{150}\)
7. \(\sqrt{5}\cdot\sqrt{20}\)
8. \(-\sqrt{3}\cdot\sqrt{48}\)
9. \(-\sqrt{2}\cdot\sqrt{242}\)
10. \(-\sqrt{5}\cdot\sqrt{245}\)
11. \(\frac{\sqrt{1280}}{\sqrt{5}}\)
12. \(\frac{\sqrt{1445}}{\sqrt{5}}\)

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Verbetersleutel

1. \(\frac{\sqrt{18}}{\sqrt{2}}=\sqrt{ \frac{18}{2}}=\sqrt{ 9}=3\)
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. \(-\frac{\sqrt{726}}{\sqrt{6}}=-\sqrt{ \frac{726}{6}}=-\sqrt{ 121}=-11\)
4. \(-\frac{\sqrt{2890}}{\sqrt{10}}=-\sqrt{ \frac{2890}{10}}=-\sqrt{ 289}=-17\)
5. \(\frac{\sqrt{90}}{\sqrt{10}}=\sqrt{ \frac{90}{10}}=\sqrt{ 9}=3\)
6. \(-\sqrt{6}\cdot\sqrt{150}=-\sqrt{6 \cdot 150}=-\sqrt{6 \cdot 6 \cdot 25}=-\sqrt{6 \cdot 6} \cdot \sqrt{25}=-6\cdot5=-30\)
7. \(\sqrt{5}\cdot\sqrt{20}=\sqrt{5 \cdot 20}=\sqrt{5 \cdot 5 \cdot 4}=\sqrt{5 \cdot 5} \cdot \sqrt{4}=5\cdot2=10\)
8. \(-\sqrt{3}\cdot\sqrt{48}=-\sqrt{3 \cdot 48}=-\sqrt{3 \cdot 3 \cdot 16}=-\sqrt{3 \cdot 3} \cdot \sqrt{16}=-3\cdot4=-12\)
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. \(-\sqrt{5}\cdot\sqrt{245}=-\sqrt{5 \cdot 245}=-\sqrt{5 \cdot 5 \cdot 49}=-\sqrt{5 \cdot 5} \cdot \sqrt{49}=-5\cdot7=-35\)
11. \(\frac{\sqrt{1280}}{\sqrt{5}}=\sqrt{ \frac{1280}{5}}=\sqrt{ 256}=16\)
12. \(\frac{\sqrt{1445}}{\sqrt{5}}=\sqrt{ \frac{1445}{5}}=\sqrt{ 289}=17\)