Rekenen met wortels (reeks 3)

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1. \(\sqrt{2}\cdot\sqrt{98}\)
2. \(-\sqrt{3}\cdot\sqrt{300}\)
3. \(-\sqrt{5}\cdot\sqrt{405}\)
4. \(-\frac{\sqrt{20}}{\sqrt{5}}\)
5. \(-\frac{\sqrt{325}}{\sqrt{13}}\)
6. \(\frac{\sqrt{338}}{\sqrt{2}}\)
7. \(\frac{\sqrt{162}}{\sqrt{2}}\)
8. \(\frac{\sqrt{700}}{\sqrt{7}}\)
9. \(-\frac{\sqrt{2548}}{\sqrt{13}}\)
10. \(-\frac{\sqrt{3328}}{\sqrt{13}}\)
11. \(\sqrt{3}\cdot\sqrt{48}\)
12. \(-\sqrt{6}\cdot\sqrt{294}\)

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Verbetersleutel

1. \(\sqrt{2}\cdot\sqrt{98}=\sqrt{2 \cdot 98}=\sqrt{2 \cdot 2 \cdot 49}=\sqrt{2 \cdot 2} \cdot \sqrt{49}=2\cdot7=14\)
2. \(-\sqrt{3}\cdot\sqrt{300}=-\sqrt{3 \cdot 300}=-\sqrt{3 \cdot 3 \cdot 100}=-\sqrt{3 \cdot 3} \cdot \sqrt{100}=-3\cdot10=-30\)
3. \(-\sqrt{5}\cdot\sqrt{405}=-\sqrt{5 \cdot 405}=-\sqrt{5 \cdot 5 \cdot 81}=-\sqrt{5 \cdot 5} \cdot \sqrt{81}=-5\cdot9=-45\)
4. \(-\frac{\sqrt{20}}{\sqrt{5}}=-\sqrt{ \frac{20}{5}}=-\sqrt{ 4}=-2\)
5. \(-\frac{\sqrt{325}}{\sqrt{13}}=-\sqrt{ \frac{325}{13}}=-\sqrt{ 25}=-5\)
6. \(\frac{\sqrt{338}}{\sqrt{2}}=\sqrt{ \frac{338}{2}}=\sqrt{ 169}=13\)
7. \(\frac{\sqrt{162}}{\sqrt{2}}=\sqrt{ \frac{162}{2}}=\sqrt{ 81}=9\)
8. \(\frac{\sqrt{700}}{\sqrt{7}}=\sqrt{ \frac{700}{7}}=\sqrt{ 100}=10\)
9. \(-\frac{\sqrt{2548}}{\sqrt{13}}=-\sqrt{ \frac{2548}{13}}=-\sqrt{ 196}=-14\)
10. \(-\frac{\sqrt{3328}}{\sqrt{13}}=-\sqrt{ \frac{3328}{13}}=-\sqrt{ 256}=-16\)
11. \(\sqrt{3}\cdot\sqrt{48}=\sqrt{3 \cdot 48}=\sqrt{3 \cdot 3 \cdot 16}=\sqrt{3 \cdot 3} \cdot \sqrt{16}=3\cdot4=12\)
12. \(-\sqrt{6}\cdot\sqrt{294}=-\sqrt{6 \cdot 294}=-\sqrt{6 \cdot 6 \cdot 49}=-\sqrt{6 \cdot 6} \cdot \sqrt{49}=-6\cdot7=-42\)