Rekenen met wortels (reeks 3)

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1. \(\sqrt{6}\cdot\sqrt{150}\)
2. \(\sqrt{2}\cdot\sqrt{162}\)
3. \(-\sqrt{3}\cdot\sqrt{192}\)
4. \(-\frac{\sqrt{1805}}{\sqrt{5}}\)
5. \(-\sqrt{6}\cdot\sqrt{726}\)
6. \(-\frac{\sqrt{1014}}{\sqrt{6}}\)
7. \(-\frac{\sqrt{150}}{\sqrt{6}}\)
8. \(\sqrt{2}\cdot\sqrt{50}\)
9. \(-\frac{\sqrt{1620}}{\sqrt{5}}\)
10. \(-\frac{\sqrt{2475}}{\sqrt{11}}\)
11. \(-\sqrt{5}\cdot\sqrt{20}\)
12. \(-\frac{\sqrt{245}}{\sqrt{5}}\)

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Verbetersleutel

1. \(\sqrt{6}\cdot\sqrt{150}=\sqrt{6 \cdot 150}=\sqrt{6 \cdot 6 \cdot 25}=\sqrt{6 \cdot 6} \cdot \sqrt{25}=6\cdot5=30\)
2. \(\sqrt{2}\cdot\sqrt{162}=\sqrt{2 \cdot 162}=\sqrt{2 \cdot 2 \cdot 81}=\sqrt{2 \cdot 2} \cdot \sqrt{81}=2\cdot9=18\)
3. \(-\sqrt{3}\cdot\sqrt{192}=-\sqrt{3 \cdot 192}=-\sqrt{3 \cdot 3 \cdot 64}=-\sqrt{3 \cdot 3} \cdot \sqrt{64}=-3\cdot8=-24\)
4. \(-\frac{\sqrt{1805}}{\sqrt{5}}=-\sqrt{ \frac{1805}{5}}=-\sqrt{ 361}=-19\)
5. \(-\sqrt{6}\cdot\sqrt{726}=-\sqrt{6 \cdot 726}=-\sqrt{6 \cdot 6 \cdot 121}=-\sqrt{6 \cdot 6} \cdot \sqrt{121}=-6\cdot11=-66\)
6. \(-\frac{\sqrt{1014}}{\sqrt{6}}=-\sqrt{ \frac{1014}{6}}=-\sqrt{ 169}=-13\)
7. \(-\frac{\sqrt{150}}{\sqrt{6}}=-\sqrt{ \frac{150}{6}}=-\sqrt{ 25}=-5\)
8. \(\sqrt{2}\cdot\sqrt{50}=\sqrt{2 \cdot 50}=\sqrt{2 \cdot 2 \cdot 25}=\sqrt{2 \cdot 2} \cdot \sqrt{25}=2\cdot5=10\)
9. \(-\frac{\sqrt{1620}}{\sqrt{5}}=-\sqrt{ \frac{1620}{5}}=-\sqrt{ 324}=-18\)
10. \(-\frac{\sqrt{2475}}{\sqrt{11}}=-\sqrt{ \frac{2475}{11}}=-\sqrt{ 225}=-15\)
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. \(-\frac{\sqrt{245}}{\sqrt{5}}=-\sqrt{ \frac{245}{5}}=-\sqrt{ 49}=-7\)