Rekenen met wortels (reeks 3)

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1. \(\frac{\sqrt{338}}{\sqrt{2}}\)
2. \(\frac{\sqrt{45}}{\sqrt{5}}\)
3. \(-\frac{\sqrt{1734}}{\sqrt{6}}\)
4. \(-\frac{\sqrt{117}}{\sqrt{13}}\)
5. \(\sqrt{3}\cdot\sqrt{363}\)
6. \(-\sqrt{6}\cdot\sqrt{726}\)
7. \(\sqrt{5}\cdot\sqrt{45}\)
8. \(-\sqrt{3}\cdot\sqrt{300}\)
9. \(-\sqrt{10}\cdot\sqrt{90}\)
10. \(\frac{\sqrt{539}}{\sqrt{11}}\)
11. \(-\frac{\sqrt{162}}{\sqrt{2}}\)
12. \(-\sqrt{5}\cdot\sqrt{320}\)

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Verbetersleutel

1. \(\frac{\sqrt{338}}{\sqrt{2}}=\sqrt{ \frac{338}{2}}=\sqrt{ 169}=13\)
2. \(\frac{\sqrt{45}}{\sqrt{5}}=\sqrt{ \frac{45}{5}}=\sqrt{ 9}=3\)
3. \(-\frac{\sqrt{1734}}{\sqrt{6}}=-\sqrt{ \frac{1734}{6}}=-\sqrt{ 289}=-17\)
4. \(-\frac{\sqrt{117}}{\sqrt{13}}=-\sqrt{ \frac{117}{13}}=-\sqrt{ 9}=-3\)
5. \(\sqrt{3}\cdot\sqrt{363}=\sqrt{3 \cdot 363}=\sqrt{3 \cdot 3 \cdot 121}=\sqrt{3 \cdot 3} \cdot \sqrt{121}=3\cdot11=33\)
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. \(\sqrt{5}\cdot\sqrt{45}=\sqrt{5 \cdot 45}=\sqrt{5 \cdot 5 \cdot 9}=\sqrt{5 \cdot 5} \cdot \sqrt{9}=5\cdot3=15\)
8. \(-\sqrt{3}\cdot\sqrt{300}=-\sqrt{3 \cdot 300}=-\sqrt{3 \cdot 3 \cdot 100}=-\sqrt{3 \cdot 3} \cdot \sqrt{100}=-3\cdot10=-30\)
9. \(-\sqrt{10}\cdot\sqrt{90}=-\sqrt{10 \cdot 90}=-\sqrt{10 \cdot 10 \cdot 9}=-\sqrt{10 \cdot 10} \cdot \sqrt{9}=-10\cdot3=-30\)
10. \(\frac{\sqrt{539}}{\sqrt{11}}=\sqrt{ \frac{539}{11}}=\sqrt{ 49}=7\)
11. \(-\frac{\sqrt{162}}{\sqrt{2}}=-\sqrt{ \frac{162}{2}}=-\sqrt{ 81}=-9\)
12. \(-\sqrt{5}\cdot\sqrt{320}=-\sqrt{5 \cdot 320}=-\sqrt{5 \cdot 5 \cdot 64}=-\sqrt{5 \cdot 5} \cdot \sqrt{64}=-5\cdot8=-40\)