Rekenen met wortels (reeks 3)

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1. \(\sqrt{2}\cdot\sqrt{50}\)
2. \(\frac{\sqrt{1734}}{\sqrt{6}}\)
3. \(\sqrt{6}\cdot\sqrt{726}\)
4. \(-\sqrt{6}\cdot\sqrt{150}\)
5. \(-\frac{\sqrt{605}}{\sqrt{5}}\)
6. \(\frac{\sqrt{704}}{\sqrt{11}}\)
7. \(-\frac{\sqrt{726}}{\sqrt{6}}\)
8. \(\frac{\sqrt{147}}{\sqrt{3}}\)
9. \(-\frac{\sqrt{99}}{\sqrt{11}}\)
10. \(\frac{\sqrt{768}}{\sqrt{3}}\)
11. \(-\frac{\sqrt{3757}}{\sqrt{13}}\)
12. \(\frac{\sqrt{90}}{\sqrt{10}}\)

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Verbetersleutel

1. \(\sqrt{2}\cdot\sqrt{50}=\sqrt{2 \cdot 50}=\sqrt{2 \cdot 2 \cdot 25}=\sqrt{2 \cdot 2} \cdot \sqrt{25}=2\cdot5=10\)
2. \(\frac{\sqrt{1734}}{\sqrt{6}}=\sqrt{ \frac{1734}{6}}=\sqrt{ 289}=17\)
3. \(\sqrt{6}\cdot\sqrt{726}=\sqrt{6 \cdot 726}=\sqrt{6 \cdot 6 \cdot 121}=\sqrt{6 \cdot 6} \cdot \sqrt{121}=6\cdot11=66\)
4. \(-\sqrt{6}\cdot\sqrt{150}=-\sqrt{6 \cdot 150}=-\sqrt{6 \cdot 6 \cdot 25}=-\sqrt{6 \cdot 6} \cdot \sqrt{25}=-6\cdot5=-30\)
5. \(-\frac{\sqrt{605}}{\sqrt{5}}=-\sqrt{ \frac{605}{5}}=-\sqrt{ 121}=-11\)
6. \(\frac{\sqrt{704}}{\sqrt{11}}=\sqrt{ \frac{704}{11}}=\sqrt{ 64}=8\)
7. \(-\frac{\sqrt{726}}{\sqrt{6}}=-\sqrt{ \frac{726}{6}}=-\sqrt{ 121}=-11\)
8. \(\frac{\sqrt{147}}{\sqrt{3}}=\sqrt{ \frac{147}{3}}=\sqrt{ 49}=7\)
9. \(-\frac{\sqrt{99}}{\sqrt{11}}=-\sqrt{ \frac{99}{11}}=-\sqrt{ 9}=-3\)
10. \(\frac{\sqrt{768}}{\sqrt{3}}=\sqrt{ \frac{768}{3}}=\sqrt{ 256}=16\)
11. \(-\frac{\sqrt{3757}}{\sqrt{13}}=-\sqrt{ \frac{3757}{13}}=-\sqrt{ 289}=-17\)
12. \(\frac{\sqrt{90}}{\sqrt{10}}=\sqrt{ \frac{90}{10}}=\sqrt{ 9}=3\)