Rekenen met wortels (reeks 3)

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1. \(\sqrt{3}\cdot\sqrt{48}\)
2. \(-\frac{\sqrt{176}}{\sqrt{11}}\)
3. \(\sqrt{6}\cdot\sqrt{150}\)
4. \(\frac{\sqrt{1734}}{\sqrt{6}}\)
5. \(\frac{\sqrt{448}}{\sqrt{7}}\)
6. \(\sqrt{6}\cdot\sqrt{726}\)
7. \(\frac{\sqrt{1210}}{\sqrt{10}}\)
8. \(-\sqrt{5}\cdot\sqrt{405}\)
9. \(-\frac{\sqrt{208}}{\sqrt{13}}\)
10. \(-\sqrt{3}\cdot\sqrt{363}\)
11. \(\frac{\sqrt{578}}{\sqrt{2}}\)
12. \(-\frac{\sqrt{1872}}{\sqrt{13}}\)

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Verbetersleutel

1. \(\sqrt{3}\cdot\sqrt{48}=\sqrt{3 \cdot 48}=\sqrt{3 \cdot 3 \cdot 16}=\sqrt{3 \cdot 3} \cdot \sqrt{16}=3\cdot4=12\)
2. \(-\frac{\sqrt{176}}{\sqrt{11}}=-\sqrt{ \frac{176}{11}}=-\sqrt{ 16}=-4\)
3. \(\sqrt{6}\cdot\sqrt{150}=\sqrt{6 \cdot 150}=\sqrt{6 \cdot 6 \cdot 25}=\sqrt{6 \cdot 6} \cdot \sqrt{25}=6\cdot5=30\)
4. \(\frac{\sqrt{1734}}{\sqrt{6}}=\sqrt{ \frac{1734}{6}}=\sqrt{ 289}=17\)
5. \(\frac{\sqrt{448}}{\sqrt{7}}=\sqrt{ \frac{448}{7}}=\sqrt{ 64}=8\)
6. \(\sqrt{6}\cdot\sqrt{726}=\sqrt{6 \cdot 726}=\sqrt{6 \cdot 6 \cdot 121}=\sqrt{6 \cdot 6} \cdot \sqrt{121}=6\cdot11=66\)
7. \(\frac{\sqrt{1210}}{\sqrt{10}}=\sqrt{ \frac{1210}{10}}=\sqrt{ 121}=11\)
8. \(-\sqrt{5}\cdot\sqrt{405}=-\sqrt{5 \cdot 405}=-\sqrt{5 \cdot 5 \cdot 81}=-\sqrt{5 \cdot 5} \cdot \sqrt{81}=-5\cdot9=-45\)
9. \(-\frac{\sqrt{208}}{\sqrt{13}}=-\sqrt{ \frac{208}{13}}=-\sqrt{ 16}=-4\)
10. \(-\sqrt{3}\cdot\sqrt{363}=-\sqrt{3 \cdot 363}=-\sqrt{3 \cdot 3 \cdot 121}=-\sqrt{3 \cdot 3} \cdot \sqrt{121}=-3\cdot11=-33\)
11. \(\frac{\sqrt{578}}{\sqrt{2}}=\sqrt{ \frac{578}{2}}=\sqrt{ 289}=17\)
12. \(-\frac{\sqrt{1872}}{\sqrt{13}}=-\sqrt{ \frac{1872}{13}}=-\sqrt{ 144}=-12\)