Rekenen met wortels (reeks 3)

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1. \(\frac{\sqrt{18}}{\sqrt{2}}\)
2. \(-\frac{\sqrt{1690}}{\sqrt{10}}\)
3. \(-\sqrt{2}\cdot\sqrt{50}\)
4. \(-\frac{\sqrt{147}}{\sqrt{3}}\)
5. \(-\frac{\sqrt{3610}}{\sqrt{10}}\)
6. \(-\frac{\sqrt{768}}{\sqrt{3}}\)
7. \(-\frac{\sqrt{117}}{\sqrt{13}}\)
8. \(-\sqrt{5}\cdot\sqrt{20}\)
9. \(\sqrt{5}\cdot\sqrt{405}\)
10. \(\sqrt{6}\cdot\sqrt{294}\)
11. \(\sqrt{3}\cdot\sqrt{12}\)
12. \(-\frac{\sqrt{847}}{\sqrt{7}}\)

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Verbetersleutel

1. \(\frac{\sqrt{18}}{\sqrt{2}}=\sqrt{ \frac{18}{2}}=\sqrt{ 9}=3\)
2. \(-\frac{\sqrt{1690}}{\sqrt{10}}=-\sqrt{ \frac{1690}{10}}=-\sqrt{ 169}=-13\)
3. \(-\sqrt{2}\cdot\sqrt{50}=-\sqrt{2 \cdot 50}=-\sqrt{2 \cdot 2 \cdot 25}=-\sqrt{2 \cdot 2} \cdot \sqrt{25}=-2\cdot5=-10\)
4. \(-\frac{\sqrt{147}}{\sqrt{3}}=-\sqrt{ \frac{147}{3}}=-\sqrt{ 49}=-7\)
5. \(-\frac{\sqrt{3610}}{\sqrt{10}}=-\sqrt{ \frac{3610}{10}}=-\sqrt{ 361}=-19\)
6. \(-\frac{\sqrt{768}}{\sqrt{3}}=-\sqrt{ \frac{768}{3}}=-\sqrt{ 256}=-16\)
7. \(-\frac{\sqrt{117}}{\sqrt{13}}=-\sqrt{ \frac{117}{13}}=-\sqrt{ 9}=-3\)
8. \(-\sqrt{5}\cdot\sqrt{20}=-\sqrt{5 \cdot 20}=-\sqrt{5 \cdot 5 \cdot 4}=-\sqrt{5 \cdot 5} \cdot \sqrt{4}=-5\cdot2=-10\)
9. \(\sqrt{5}\cdot\sqrt{405}=\sqrt{5 \cdot 405}=\sqrt{5 \cdot 5 \cdot 81}=\sqrt{5 \cdot 5} \cdot \sqrt{81}=5\cdot9=45\)
10. \(\sqrt{6}\cdot\sqrt{294}=\sqrt{6 \cdot 294}=\sqrt{6 \cdot 6 \cdot 49}=\sqrt{6 \cdot 6} \cdot \sqrt{49}=6\cdot7=42\)
11. \(\sqrt{3}\cdot\sqrt{12}=\sqrt{3 \cdot 12}=\sqrt{3 \cdot 3 \cdot 4}=\sqrt{3 \cdot 3} \cdot \sqrt{4}=3\cdot2=6\)
12. \(-\frac{\sqrt{847}}{\sqrt{7}}=-\sqrt{ \frac{847}{7}}=-\sqrt{ 121}=-11\)