Rekenen met wortels (reeks 3)

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1. \(\sqrt{2}\cdot\sqrt{162}\)
2. \(-\frac{\sqrt{50}}{\sqrt{2}}\)
3. \(\sqrt{10}\cdot\sqrt{810}\)
4. \(-\frac{\sqrt{242}}{\sqrt{2}}\)
5. \(-\frac{\sqrt{1200}}{\sqrt{3}}\)
6. \(\frac{\sqrt{637}}{\sqrt{13}}\)
7. \(\frac{\sqrt{2156}}{\sqrt{11}}\)
8. \(-\sqrt{5}\cdot\sqrt{405}\)
9. \(\sqrt{3}\cdot\sqrt{363}\)
10. \(-\frac{\sqrt{810}}{\sqrt{10}}\)
11. \(\sqrt{2}\cdot\sqrt{50}\)
12. \(\sqrt{3}\cdot\sqrt{300}\)

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Verbetersleutel

1. \(\sqrt{2}\cdot\sqrt{162}=\sqrt{2 \cdot 162}=\sqrt{2 \cdot 2 \cdot 81}=\sqrt{2 \cdot 2} \cdot \sqrt{81}=2\cdot9=18\)
2. \(-\frac{\sqrt{50}}{\sqrt{2}}=-\sqrt{ \frac{50}{2}}=-\sqrt{ 25}=-5\)
3. \(\sqrt{10}\cdot\sqrt{810}=\sqrt{10 \cdot 810}=\sqrt{10 \cdot 10 \cdot 81}=\sqrt{10 \cdot 10} \cdot \sqrt{81}=10\cdot9=90\)
4. \(-\frac{\sqrt{242}}{\sqrt{2}}=-\sqrt{ \frac{242}{2}}=-\sqrt{ 121}=-11\)
5. \(-\frac{\sqrt{1200}}{\sqrt{3}}=-\sqrt{ \frac{1200}{3}}=-\sqrt{ 400}=-20\)
6. \(\frac{\sqrt{637}}{\sqrt{13}}=\sqrt{ \frac{637}{13}}=\sqrt{ 49}=7\)
7. \(\frac{\sqrt{2156}}{\sqrt{11}}=\sqrt{ \frac{2156}{11}}=\sqrt{ 196}=14\)
8. \(-\sqrt{5}\cdot\sqrt{405}=-\sqrt{5 \cdot 405}=-\sqrt{5 \cdot 5 \cdot 81}=-\sqrt{5 \cdot 5} \cdot \sqrt{81}=-5\cdot9=-45\)
9. \(\sqrt{3}\cdot\sqrt{363}=\sqrt{3 \cdot 363}=\sqrt{3 \cdot 3 \cdot 121}=\sqrt{3 \cdot 3} \cdot \sqrt{121}=3\cdot11=33\)
10. \(-\frac{\sqrt{810}}{\sqrt{10}}=-\sqrt{ \frac{810}{10}}=-\sqrt{ 81}=-9\)
11. \(\sqrt{2}\cdot\sqrt{50}=\sqrt{2 \cdot 50}=\sqrt{2 \cdot 2 \cdot 25}=\sqrt{2 \cdot 2} \cdot \sqrt{25}=2\cdot5=10\)
12. \(\sqrt{3}\cdot\sqrt{300}=\sqrt{3 \cdot 300}=\sqrt{3 \cdot 3 \cdot 100}=\sqrt{3 \cdot 3} \cdot \sqrt{100}=3\cdot10=30\)