Rekenen met wortels (reeks 3)

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1. \(\sqrt{5}\cdot\sqrt{245}\)
2. \(-\sqrt{2}\cdot\sqrt{242}\)
3. \(-\sqrt{3}\cdot\sqrt{12}\)
4. \(\sqrt{5}\cdot\sqrt{80}\)
5. \(-\frac{\sqrt{810}}{\sqrt{10}}\)
6. \(\frac{\sqrt{2166}}{\sqrt{6}}\)
7. \(-\sqrt{3}\cdot\sqrt{48}\)
8. \(\sqrt{3}\cdot\sqrt{192}\)
9. \(-\sqrt{6}\cdot\sqrt{726}\)
10. \(\sqrt{2}\cdot\sqrt{18}\)
11. \(\frac{\sqrt{363}}{\sqrt{3}}\)
12. \(\frac{\sqrt{1100}}{\sqrt{11}}\)

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Verbetersleutel

1. \(\sqrt{5}\cdot\sqrt{245}=\sqrt{5 \cdot 245}=\sqrt{5 \cdot 5 \cdot 49}=\sqrt{5 \cdot 5} \cdot \sqrt{49}=5\cdot7=35\)
2. \(-\sqrt{2}\cdot\sqrt{242}=-\sqrt{2 \cdot 242}=-\sqrt{2 \cdot 2 \cdot 121}=-\sqrt{2 \cdot 2} \cdot \sqrt{121}=-2\cdot11=-22\)
3. \(-\sqrt{3}\cdot\sqrt{12}=-\sqrt{3 \cdot 12}=-\sqrt{3 \cdot 3 \cdot 4}=-\sqrt{3 \cdot 3} \cdot \sqrt{4}=-3\cdot2=-6\)
4. \(\sqrt{5}\cdot\sqrt{80}=\sqrt{5 \cdot 80}=\sqrt{5 \cdot 5 \cdot 16}=\sqrt{5 \cdot 5} \cdot \sqrt{16}=5\cdot4=20\)
5. \(-\frac{\sqrt{810}}{\sqrt{10}}=-\sqrt{ \frac{810}{10}}=-\sqrt{ 81}=-9\)
6. \(\frac{\sqrt{2166}}{\sqrt{6}}=\sqrt{ \frac{2166}{6}}=\sqrt{ 361}=19\)
7. \(-\sqrt{3}\cdot\sqrt{48}=-\sqrt{3 \cdot 48}=-\sqrt{3 \cdot 3 \cdot 16}=-\sqrt{3 \cdot 3} \cdot \sqrt{16}=-3\cdot4=-12\)
8. \(\sqrt{3}\cdot\sqrt{192}=\sqrt{3 \cdot 192}=\sqrt{3 \cdot 3 \cdot 64}=\sqrt{3 \cdot 3} \cdot \sqrt{64}=3\cdot8=24\)
9. \(-\sqrt{6}\cdot\sqrt{726}=-\sqrt{6 \cdot 726}=-\sqrt{6 \cdot 6 \cdot 121}=-\sqrt{6 \cdot 6} \cdot \sqrt{121}=-6\cdot11=-66\)
10. \(\sqrt{2}\cdot\sqrt{18}=\sqrt{2 \cdot 18}=\sqrt{2 \cdot 2 \cdot 9}=\sqrt{2 \cdot 2} \cdot \sqrt{9}=2\cdot3=6\)
11. \(\frac{\sqrt{363}}{\sqrt{3}}=\sqrt{ \frac{363}{3}}=\sqrt{ 121}=11\)
12. \(\frac{\sqrt{1100}}{\sqrt{11}}=\sqrt{ \frac{1100}{11}}=\sqrt{ 100}=10\)