Rekenen met wortels (reeks 3)

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1. \(\sqrt{3}\cdot\sqrt{48}\)
2. \(\sqrt{5}\cdot\sqrt{180}\)
3. \(-\sqrt{10}\cdot\sqrt{1210}\)
4. \(-\frac{\sqrt{1734}}{\sqrt{6}}\)
5. \(-\sqrt{5}\cdot\sqrt{605}\)
6. \(\frac{\sqrt{845}}{\sqrt{5}}\)
7. \(-\sqrt{10}\cdot\sqrt{490}\)
8. \(\frac{\sqrt{242}}{\sqrt{2}}\)
9. \(\frac{\sqrt{1014}}{\sqrt{6}}\)
10. \(-\sqrt{3}\cdot\sqrt{363}\)
11. \(\sqrt{6}\cdot\sqrt{294}\)
12. \(-\frac{\sqrt{150}}{\sqrt{6}}\)

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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. \(\sqrt{5}\cdot\sqrt{180}=\sqrt{5 \cdot 180}=\sqrt{5 \cdot 5 \cdot 36}=\sqrt{5 \cdot 5} \cdot \sqrt{36}=5\cdot6=30\)
3. \(-\sqrt{10}\cdot\sqrt{1210}=-\sqrt{10 \cdot 1210}=-\sqrt{10 \cdot 10 \cdot 121}=-\sqrt{10 \cdot 10} \cdot \sqrt{121}=-10\cdot11=-110\)
4. \(-\frac{\sqrt{1734}}{\sqrt{6}}=-\sqrt{ \frac{1734}{6}}=-\sqrt{ 289}=-17\)
5. \(-\sqrt{5}\cdot\sqrt{605}=-\sqrt{5 \cdot 605}=-\sqrt{5 \cdot 5 \cdot 121}=-\sqrt{5 \cdot 5} \cdot \sqrt{121}=-5\cdot11=-55\)
6. \(\frac{\sqrt{845}}{\sqrt{5}}=\sqrt{ \frac{845}{5}}=\sqrt{ 169}=13\)
7. \(-\sqrt{10}\cdot\sqrt{490}=-\sqrt{10 \cdot 490}=-\sqrt{10 \cdot 10 \cdot 49}=-\sqrt{10 \cdot 10} \cdot \sqrt{49}=-10\cdot7=-70\)
8. \(\frac{\sqrt{242}}{\sqrt{2}}=\sqrt{ \frac{242}{2}}=\sqrt{ 121}=11\)
9. \(\frac{\sqrt{1014}}{\sqrt{6}}=\sqrt{ \frac{1014}{6}}=\sqrt{ 169}=13\)
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. \(\sqrt{6}\cdot\sqrt{294}=\sqrt{6 \cdot 294}=\sqrt{6 \cdot 6 \cdot 49}=\sqrt{6 \cdot 6} \cdot \sqrt{49}=6\cdot7=42\)
12. \(-\frac{\sqrt{150}}{\sqrt{6}}=-\sqrt{ \frac{150}{6}}=-\sqrt{ 25}=-5\)