Rekenen met wortels (reeks 3)

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1. \(-\frac{\sqrt{44}}{\sqrt{11}}\)
2. \(\frac{\sqrt{1300}}{\sqrt{13}}\)
3. \(-\frac{\sqrt{150}}{\sqrt{6}}\)
4. \(\sqrt{5}\cdot\sqrt{80}\)
5. \(-\frac{\sqrt{3610}}{\sqrt{10}}\)
6. \(-\sqrt{6}\cdot\sqrt{150}\)
7. \(\frac{\sqrt{192}}{\sqrt{3}}\)
8. \(\frac{\sqrt{1573}}{\sqrt{13}}\)
9. \(\frac{\sqrt{847}}{\sqrt{7}}\)
10. \(-\sqrt{3}\cdot\sqrt{12}\)
11. \(\frac{\sqrt{1083}}{\sqrt{3}}\)
12. \(-\sqrt{3}\cdot\sqrt{300}\)

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Verbetersleutel

1. \(-\frac{\sqrt{44}}{\sqrt{11}}=-\sqrt{ \frac{44}{11}}=-\sqrt{ 4}=-2\)
2. \(\frac{\sqrt{1300}}{\sqrt{13}}=\sqrt{ \frac{1300}{13}}=\sqrt{ 100}=10\)
3. \(-\frac{\sqrt{150}}{\sqrt{6}}=-\sqrt{ \frac{150}{6}}=-\sqrt{ 25}=-5\)
4. \(\sqrt{5}\cdot\sqrt{80}=\sqrt{5 \cdot 80}=\sqrt{5 \cdot 5 \cdot 16}=\sqrt{5 \cdot 5} \cdot \sqrt{16}=5\cdot4=20\)
5. \(-\frac{\sqrt{3610}}{\sqrt{10}}=-\sqrt{ \frac{3610}{10}}=-\sqrt{ 361}=-19\)
6. \(-\sqrt{6}\cdot\sqrt{150}=-\sqrt{6 \cdot 150}=-\sqrt{6 \cdot 6 \cdot 25}=-\sqrt{6 \cdot 6} \cdot \sqrt{25}=-6\cdot5=-30\)
7. \(\frac{\sqrt{192}}{\sqrt{3}}=\sqrt{ \frac{192}{3}}=\sqrt{ 64}=8\)
8. \(\frac{\sqrt{1573}}{\sqrt{13}}=\sqrt{ \frac{1573}{13}}=\sqrt{ 121}=11\)
9. \(\frac{\sqrt{847}}{\sqrt{7}}=\sqrt{ \frac{847}{7}}=\sqrt{ 121}=11\)
10. \(-\sqrt{3}\cdot\sqrt{12}=-\sqrt{3 \cdot 12}=-\sqrt{3 \cdot 3 \cdot 4}=-\sqrt{3 \cdot 3} \cdot \sqrt{4}=-3\cdot2=-6\)
11. \(\frac{\sqrt{1083}}{\sqrt{3}}=\sqrt{ \frac{1083}{3}}=\sqrt{ 361}=19\)
12. \(-\sqrt{3}\cdot\sqrt{300}=-\sqrt{3 \cdot 300}=-\sqrt{3 \cdot 3 \cdot 100}=-\sqrt{3 \cdot 3} \cdot \sqrt{100}=-3\cdot10=-30\)