Rekenen met wortels (reeks 3)

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1. \(\sqrt{10}\cdot\sqrt{1210}\)
2. \(-\frac{\sqrt{1083}}{\sqrt{3}}\)
3. \(\frac{\sqrt{450}}{\sqrt{2}}\)
4. \(-\frac{\sqrt{1280}}{\sqrt{5}}\)
5. \(-\frac{\sqrt{18}}{\sqrt{2}}\)
6. \(-\sqrt{2}\cdot\sqrt{242}\)
7. \(-\sqrt{3}\cdot\sqrt{147}\)
8. \(\frac{\sqrt{578}}{\sqrt{2}}\)
9. \(-\frac{\sqrt{162}}{\sqrt{2}}\)
10. \(\frac{\sqrt{294}}{\sqrt{6}}\)
11. \(\sqrt{2}\cdot\sqrt{18}\)
12. \(-\frac{\sqrt{1872}}{\sqrt{13}}\)

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Verbetersleutel

1. \(\sqrt{10}\cdot\sqrt{1210}=\sqrt{10 \cdot 1210}=\sqrt{10 \cdot 10 \cdot 121}=\sqrt{10 \cdot 10} \cdot \sqrt{121}=10\cdot11=110\)
2. \(-\frac{\sqrt{1083}}{\sqrt{3}}=-\sqrt{ \frac{1083}{3}}=-\sqrt{ 361}=-19\)
3. \(\frac{\sqrt{450}}{\sqrt{2}}=\sqrt{ \frac{450}{2}}=\sqrt{ 225}=15\)
4. \(-\frac{\sqrt{1280}}{\sqrt{5}}=-\sqrt{ \frac{1280}{5}}=-\sqrt{ 256}=-16\)
5. \(-\frac{\sqrt{18}}{\sqrt{2}}=-\sqrt{ \frac{18}{2}}=-\sqrt{ 9}=-3\)
6. \(-\sqrt{2}\cdot\sqrt{242}=-\sqrt{2 \cdot 242}=-\sqrt{2 \cdot 2 \cdot 121}=-\sqrt{2 \cdot 2} \cdot \sqrt{121}=-2\cdot11=-22\)
7. \(-\sqrt{3}\cdot\sqrt{147}=-\sqrt{3 \cdot 147}=-\sqrt{3 \cdot 3 \cdot 49}=-\sqrt{3 \cdot 3} \cdot \sqrt{49}=-3\cdot7=-21\)
8. \(\frac{\sqrt{578}}{\sqrt{2}}=\sqrt{ \frac{578}{2}}=\sqrt{ 289}=17\)
9. \(-\frac{\sqrt{162}}{\sqrt{2}}=-\sqrt{ \frac{162}{2}}=-\sqrt{ 81}=-9\)
10. \(\frac{\sqrt{294}}{\sqrt{6}}=\sqrt{ \frac{294}{6}}=\sqrt{ 49}=7\)
11. \(\sqrt{2}\cdot\sqrt{18}=\sqrt{2 \cdot 18}=\sqrt{2 \cdot 2 \cdot 9}=\sqrt{2 \cdot 2} \cdot \sqrt{9}=2\cdot3=6\)
12. \(-\frac{\sqrt{1872}}{\sqrt{13}}=-\sqrt{ \frac{1872}{13}}=-\sqrt{ 144}=-12\)