Rekenen met wortels (reeks 3)

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1. \(\sqrt{10}\cdot\sqrt{90}\)
2. \(\sqrt{3}\cdot\sqrt{48}\)
3. \(\frac{\sqrt{242}}{\sqrt{2}}\)
4. \(-\sqrt{6}\cdot\sqrt{294}\)
5. \(\sqrt{10}\cdot\sqrt{1210}\)
6. \(\sqrt{5}\cdot\sqrt{45}\)
7. \(-\frac{\sqrt{700}}{\sqrt{7}}\)
8. \(\sqrt{5}\cdot\sqrt{245}\)
9. \(\frac{\sqrt{363}}{\sqrt{3}}\)
10. \(\sqrt{2}\cdot\sqrt{98}\)
11. \(-\sqrt{5}\cdot\sqrt{20}\)
12. \(\frac{\sqrt{405}}{\sqrt{5}}\)

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Verbetersleutel

1. \(\sqrt{10}\cdot\sqrt{90}=\sqrt{10 \cdot 90}=\sqrt{10 \cdot 10 \cdot 9}=\sqrt{10 \cdot 10} \cdot \sqrt{9}=10\cdot3=30\)
2. \(\sqrt{3}\cdot\sqrt{48}=\sqrt{3 \cdot 48}=\sqrt{3 \cdot 3 \cdot 16}=\sqrt{3 \cdot 3} \cdot \sqrt{16}=3\cdot4=12\)
3. \(\frac{\sqrt{242}}{\sqrt{2}}=\sqrt{ \frac{242}{2}}=\sqrt{ 121}=11\)
4. \(-\sqrt{6}\cdot\sqrt{294}=-\sqrt{6 \cdot 294}=-\sqrt{6 \cdot 6 \cdot 49}=-\sqrt{6 \cdot 6} \cdot \sqrt{49}=-6\cdot7=-42\)
5. \(\sqrt{10}\cdot\sqrt{1210}=\sqrt{10 \cdot 1210}=\sqrt{10 \cdot 10 \cdot 121}=\sqrt{10 \cdot 10} \cdot \sqrt{121}=10\cdot11=110\)
6. \(\sqrt{5}\cdot\sqrt{45}=\sqrt{5 \cdot 45}=\sqrt{5 \cdot 5 \cdot 9}=\sqrt{5 \cdot 5} \cdot \sqrt{9}=5\cdot3=15\)
7. \(-\frac{\sqrt{700}}{\sqrt{7}}=-\sqrt{ \frac{700}{7}}=-\sqrt{ 100}=-10\)
8. \(\sqrt{5}\cdot\sqrt{245}=\sqrt{5 \cdot 245}=\sqrt{5 \cdot 5 \cdot 49}=\sqrt{5 \cdot 5} \cdot \sqrt{49}=5\cdot7=35\)
9. \(\frac{\sqrt{363}}{\sqrt{3}}=\sqrt{ \frac{363}{3}}=\sqrt{ 121}=11\)
10. \(\sqrt{2}\cdot\sqrt{98}=\sqrt{2 \cdot 98}=\sqrt{2 \cdot 2 \cdot 49}=\sqrt{2 \cdot 2} \cdot \sqrt{49}=2\cdot7=14\)
11. \(-\sqrt{5}\cdot\sqrt{20}=-\sqrt{5 \cdot 20}=-\sqrt{5 \cdot 5 \cdot 4}=-\sqrt{5 \cdot 5} \cdot \sqrt{4}=-5\cdot2=-10\)
12. \(\frac{\sqrt{405}}{\sqrt{5}}=\sqrt{ \frac{405}{5}}=\sqrt{ 81}=9\)