Rekenen met wortels (reeks 3)

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1. \(-\sqrt{5}\cdot\sqrt{180}\)
2. \(-\sqrt{10}\cdot\sqrt{1210}\)
3. \(\frac{\sqrt{112}}{\sqrt{7}}\)
4. \(\frac{\sqrt{1280}}{\sqrt{5}}\)
5. \(\frac{\sqrt{578}}{\sqrt{2}}\)
6. \(\sqrt{3}\cdot\sqrt{75}\)
7. \(\frac{\sqrt{490}}{\sqrt{10}}\)
8. \(-\sqrt{10}\cdot\sqrt{490}\)
9. \(-\frac{\sqrt{75}}{\sqrt{3}}\)
10. \(-\sqrt{6}\cdot\sqrt{726}\)
11. \(-\sqrt{2}\cdot\sqrt{98}\)
12. \(\frac{\sqrt{117}}{\sqrt{13}}\)

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Verbetersleutel

1. \(-\sqrt{5}\cdot\sqrt{180}=-\sqrt{5 \cdot 180}=-\sqrt{5 \cdot 5 \cdot 36}=-\sqrt{5 \cdot 5} \cdot \sqrt{36}=-5\cdot6=-30\)
2. \(-\sqrt{10}\cdot\sqrt{1210}=-\sqrt{10 \cdot 1210}=-\sqrt{10 \cdot 10 \cdot 121}=-\sqrt{10 \cdot 10} \cdot \sqrt{121}=-10\cdot11=-110\)
3. \(\frac{\sqrt{112}}{\sqrt{7}}=\sqrt{ \frac{112}{7}}=\sqrt{ 16}=4\)
4. \(\frac{\sqrt{1280}}{\sqrt{5}}=\sqrt{ \frac{1280}{5}}=\sqrt{ 256}=16\)
5. \(\frac{\sqrt{578}}{\sqrt{2}}=\sqrt{ \frac{578}{2}}=\sqrt{ 289}=17\)
6. \(\sqrt{3}\cdot\sqrt{75}=\sqrt{3 \cdot 75}=\sqrt{3 \cdot 3 \cdot 25}=\sqrt{3 \cdot 3} \cdot \sqrt{25}=3\cdot5=15\)
7. \(\frac{\sqrt{490}}{\sqrt{10}}=\sqrt{ \frac{490}{10}}=\sqrt{ 49}=7\)
8. \(-\sqrt{10}\cdot\sqrt{490}=-\sqrt{10 \cdot 490}=-\sqrt{10 \cdot 10 \cdot 49}=-\sqrt{10 \cdot 10} \cdot \sqrt{49}=-10\cdot7=-70\)
9. \(-\frac{\sqrt{75}}{\sqrt{3}}=-\sqrt{ \frac{75}{3}}=-\sqrt{ 25}=-5\)
10. \(-\sqrt{6}\cdot\sqrt{726}=-\sqrt{6 \cdot 726}=-\sqrt{6 \cdot 6 \cdot 121}=-\sqrt{6 \cdot 6} \cdot \sqrt{121}=-6\cdot11=-66\)
11. \(-\sqrt{2}\cdot\sqrt{98}=-\sqrt{2 \cdot 98}=-\sqrt{2 \cdot 2 \cdot 49}=-\sqrt{2 \cdot 2} \cdot \sqrt{49}=-2\cdot7=-14\)
12. \(\frac{\sqrt{117}}{\sqrt{13}}=\sqrt{ \frac{117}{13}}=\sqrt{ 9}=3\)