Rekenen met wortels (reeks 3)

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1. \(\sqrt{6}\cdot\sqrt{294}\)
2. \(\sqrt{6}\cdot\sqrt{726}\)
3. \(\sqrt{2}\cdot\sqrt{98}\)
4. \(\frac{\sqrt{75}}{\sqrt{3}}\)
5. \(\frac{\sqrt{2925}}{\sqrt{13}}\)
6. \(\frac{\sqrt{490}}{\sqrt{10}}\)
7. \(\sqrt{3}\cdot\sqrt{300}\)
8. \(-\frac{\sqrt{1690}}{\sqrt{10}}\)
9. \(\frac{\sqrt{98}}{\sqrt{2}}\)
10. \(\frac{\sqrt{90}}{\sqrt{10}}\)
11. \(-\frac{\sqrt{20}}{\sqrt{5}}\)
12. \(\frac{\sqrt{294}}{\sqrt{6}}\)

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Verbetersleutel

1. \(\sqrt{6}\cdot\sqrt{294}=\sqrt{6 \cdot 294}=\sqrt{6 \cdot 6 \cdot 49}=\sqrt{6 \cdot 6} \cdot \sqrt{49}=6\cdot7=42\)
2. \(\sqrt{6}\cdot\sqrt{726}=\sqrt{6 \cdot 726}=\sqrt{6 \cdot 6 \cdot 121}=\sqrt{6 \cdot 6} \cdot \sqrt{121}=6\cdot11=66\)
3. \(\sqrt{2}\cdot\sqrt{98}=\sqrt{2 \cdot 98}=\sqrt{2 \cdot 2 \cdot 49}=\sqrt{2 \cdot 2} \cdot \sqrt{49}=2\cdot7=14\)
4. \(\frac{\sqrt{75}}{\sqrt{3}}=\sqrt{ \frac{75}{3}}=\sqrt{ 25}=5\)
5. \(\frac{\sqrt{2925}}{\sqrt{13}}=\sqrt{ \frac{2925}{13}}=\sqrt{ 225}=15\)
6. \(\frac{\sqrt{490}}{\sqrt{10}}=\sqrt{ \frac{490}{10}}=\sqrt{ 49}=7\)
7. \(\sqrt{3}\cdot\sqrt{300}=\sqrt{3 \cdot 300}=\sqrt{3 \cdot 3 \cdot 100}=\sqrt{3 \cdot 3} \cdot \sqrt{100}=3\cdot10=30\)
8. \(-\frac{\sqrt{1690}}{\sqrt{10}}=-\sqrt{ \frac{1690}{10}}=-\sqrt{ 169}=-13\)
9. \(\frac{\sqrt{98}}{\sqrt{2}}=\sqrt{ \frac{98}{2}}=\sqrt{ 49}=7\)
10. \(\frac{\sqrt{90}}{\sqrt{10}}=\sqrt{ \frac{90}{10}}=\sqrt{ 9}=3\)
11. \(-\frac{\sqrt{20}}{\sqrt{5}}=-\sqrt{ \frac{20}{5}}=-\sqrt{ 4}=-2\)
12. \(\frac{\sqrt{294}}{\sqrt{6}}=\sqrt{ \frac{294}{6}}=\sqrt{ 49}=7\)