Rekenen met wortels (reeks 3)

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1. \(-\sqrt{3}\cdot\sqrt{75}\)
2. \(-\frac{\sqrt{275}}{\sqrt{11}}\)
3. \(\frac{\sqrt{490}}{\sqrt{10}}\)
4. \(-\sqrt{3}\cdot\sqrt{48}\)
5. \(\sqrt{3}\cdot\sqrt{147}\)
6. \(\frac{\sqrt{300}}{\sqrt{3}}\)
7. \(\frac{\sqrt{3564}}{\sqrt{11}}\)
8. \(\frac{\sqrt{2166}}{\sqrt{6}}\)
9. \(\frac{\sqrt{147}}{\sqrt{3}}\)
10. \(\sqrt{5}\cdot\sqrt{180}\)
11. \(-\frac{\sqrt{50}}{\sqrt{2}}\)
12. \(-\sqrt{10}\cdot\sqrt{90}\)

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Verbetersleutel

1. \(-\sqrt{3}\cdot\sqrt{75}=-\sqrt{3 \cdot 75}=-\sqrt{3 \cdot 3 \cdot 25}=-\sqrt{3 \cdot 3} \cdot \sqrt{25}=-3\cdot5=-15\)
2. \(-\frac{\sqrt{275}}{\sqrt{11}}=-\sqrt{ \frac{275}{11}}=-\sqrt{ 25}=-5\)
3. \(\frac{\sqrt{490}}{\sqrt{10}}=\sqrt{ \frac{490}{10}}=\sqrt{ 49}=7\)
4. \(-\sqrt{3}\cdot\sqrt{48}=-\sqrt{3 \cdot 48}=-\sqrt{3 \cdot 3 \cdot 16}=-\sqrt{3 \cdot 3} \cdot \sqrt{16}=-3\cdot4=-12\)
5. \(\sqrt{3}\cdot\sqrt{147}=\sqrt{3 \cdot 147}=\sqrt{3 \cdot 3 \cdot 49}=\sqrt{3 \cdot 3} \cdot \sqrt{49}=3\cdot7=21\)
6. \(\frac{\sqrt{300}}{\sqrt{3}}=\sqrt{ \frac{300}{3}}=\sqrt{ 100}=10\)
7. \(\frac{\sqrt{3564}}{\sqrt{11}}=\sqrt{ \frac{3564}{11}}=\sqrt{ 324}=18\)
8. \(\frac{\sqrt{2166}}{\sqrt{6}}=\sqrt{ \frac{2166}{6}}=\sqrt{ 361}=19\)
9. \(\frac{\sqrt{147}}{\sqrt{3}}=\sqrt{ \frac{147}{3}}=\sqrt{ 49}=7\)
10. \(\sqrt{5}\cdot\sqrt{180}=\sqrt{5 \cdot 180}=\sqrt{5 \cdot 5 \cdot 36}=\sqrt{5 \cdot 5} \cdot \sqrt{36}=5\cdot6=30\)
11. \(-\frac{\sqrt{50}}{\sqrt{2}}=-\sqrt{ \frac{50}{2}}=-\sqrt{ 25}=-5\)
12. \(-\sqrt{10}\cdot\sqrt{90}=-\sqrt{10 \cdot 90}=-\sqrt{10 \cdot 10 \cdot 9}=-\sqrt{10 \cdot 10} \cdot \sqrt{9}=-10\cdot3=-30\)