Rekenen met wortels (reeks 3)

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1. \(\sqrt{5}\cdot\sqrt{45}\)
2. \(\frac{\sqrt{242}}{\sqrt{2}}\)
3. \(\sqrt{3}\cdot\sqrt{192}\)
4. \(-\frac{\sqrt{3564}}{\sqrt{11}}\)
5. \(\frac{\sqrt{832}}{\sqrt{13}}\)
6. \(\sqrt{2}\cdot\sqrt{18}\)
7. \(\sqrt{6}\cdot\sqrt{294}\)
8. \(-\frac{\sqrt{1805}}{\sqrt{5}}\)
9. \(\sqrt{3}\cdot\sqrt{48}\)
10. \(-\frac{\sqrt{294}}{\sqrt{6}}\)
11. \(-\frac{\sqrt{192}}{\sqrt{3}}\)
12. \(\sqrt{5}\cdot\sqrt{320}\)

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Verbetersleutel

1. \(\sqrt{5}\cdot\sqrt{45}=\sqrt{5 \cdot 45}=\sqrt{5 \cdot 5 \cdot 9}=\sqrt{5 \cdot 5} \cdot \sqrt{9}=5\cdot3=15\)
2. \(\frac{\sqrt{242}}{\sqrt{2}}=\sqrt{ \frac{242}{2}}=\sqrt{ 121}=11\)
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. \(-\frac{\sqrt{3564}}{\sqrt{11}}=-\sqrt{ \frac{3564}{11}}=-\sqrt{ 324}=-18\)
5. \(\frac{\sqrt{832}}{\sqrt{13}}=\sqrt{ \frac{832}{13}}=\sqrt{ 64}=8\)
6. \(\sqrt{2}\cdot\sqrt{18}=\sqrt{2 \cdot 18}=\sqrt{2 \cdot 2 \cdot 9}=\sqrt{2 \cdot 2} \cdot \sqrt{9}=2\cdot3=6\)
7. \(\sqrt{6}\cdot\sqrt{294}=\sqrt{6 \cdot 294}=\sqrt{6 \cdot 6 \cdot 49}=\sqrt{6 \cdot 6} \cdot \sqrt{49}=6\cdot7=42\)
8. \(-\frac{\sqrt{1805}}{\sqrt{5}}=-\sqrt{ \frac{1805}{5}}=-\sqrt{ 361}=-19\)
9. \(\sqrt{3}\cdot\sqrt{48}=\sqrt{3 \cdot 48}=\sqrt{3 \cdot 3 \cdot 16}=\sqrt{3 \cdot 3} \cdot \sqrt{16}=3\cdot4=12\)
10. \(-\frac{\sqrt{294}}{\sqrt{6}}=-\sqrt{ \frac{294}{6}}=-\sqrt{ 49}=-7\)
11. \(-\frac{\sqrt{192}}{\sqrt{3}}=-\sqrt{ \frac{192}{3}}=-\sqrt{ 64}=-8\)
12. \(\sqrt{5}\cdot\sqrt{320}=\sqrt{5 \cdot 320}=\sqrt{5 \cdot 5 \cdot 64}=\sqrt{5 \cdot 5} \cdot \sqrt{64}=5\cdot8=40\)