Rekenen met wortels (reeks 3)

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1. \(-\frac{\sqrt{208}}{\sqrt{13}}\)
2. \(\frac{\sqrt{1573}}{\sqrt{13}}\)
3. \(\sqrt{2}\cdot\sqrt{242}\)
4. \(-\frac{\sqrt{20}}{\sqrt{5}}\)
5. \(-\frac{\sqrt{1014}}{\sqrt{6}}\)
6. \(-\frac{\sqrt{2890}}{\sqrt{10}}\)
7. \(-\sqrt{10}\cdot\sqrt{90}\)
8. \(\frac{\sqrt{48}}{\sqrt{3}}\)
9. \(-\sqrt{5}\cdot\sqrt{45}\)
10. \(-\frac{\sqrt{3610}}{\sqrt{10}}\)
11. \(\frac{\sqrt{338}}{\sqrt{2}}\)
12. \(\sqrt{5}\cdot\sqrt{605}\)

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Verbetersleutel

1. \(-\frac{\sqrt{208}}{\sqrt{13}}=-\sqrt{ \frac{208}{13}}=-\sqrt{ 16}=-4\)
2. \(\frac{\sqrt{1573}}{\sqrt{13}}=\sqrt{ \frac{1573}{13}}=\sqrt{ 121}=11\)
3. \(\sqrt{2}\cdot\sqrt{242}=\sqrt{2 \cdot 242}=\sqrt{2 \cdot 2 \cdot 121}=\sqrt{2 \cdot 2} \cdot \sqrt{121}=2\cdot11=22\)
4. \(-\frac{\sqrt{20}}{\sqrt{5}}=-\sqrt{ \frac{20}{5}}=-\sqrt{ 4}=-2\)
5. \(-\frac{\sqrt{1014}}{\sqrt{6}}=-\sqrt{ \frac{1014}{6}}=-\sqrt{ 169}=-13\)
6. \(-\frac{\sqrt{2890}}{\sqrt{10}}=-\sqrt{ \frac{2890}{10}}=-\sqrt{ 289}=-17\)
7. \(-\sqrt{10}\cdot\sqrt{90}=-\sqrt{10 \cdot 90}=-\sqrt{10 \cdot 10 \cdot 9}=-\sqrt{10 \cdot 10} \cdot \sqrt{9}=-10\cdot3=-30\)
8. \(\frac{\sqrt{48}}{\sqrt{3}}=\sqrt{ \frac{48}{3}}=\sqrt{ 16}=4\)
9. \(-\sqrt{5}\cdot\sqrt{45}=-\sqrt{5 \cdot 45}=-\sqrt{5 \cdot 5 \cdot 9}=-\sqrt{5 \cdot 5} \cdot \sqrt{9}=-5\cdot3=-15\)
10. \(-\frac{\sqrt{3610}}{\sqrt{10}}=-\sqrt{ \frac{3610}{10}}=-\sqrt{ 361}=-19\)
11. \(\frac{\sqrt{338}}{\sqrt{2}}=\sqrt{ \frac{338}{2}}=\sqrt{ 169}=13\)
12. \(\sqrt{5}\cdot\sqrt{605}=\sqrt{5 \cdot 605}=\sqrt{5 \cdot 5 \cdot 121}=\sqrt{5 \cdot 5} \cdot \sqrt{121}=5\cdot11=55\)