Rekenen met wortels (reeks 3)

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1. \(-\frac{\sqrt{12}}{\sqrt{3}}\)
2. \(\sqrt{3}\cdot\sqrt{192}\)
3. \(-\sqrt{5}\cdot\sqrt{605}\)
4. \(-\sqrt{6}\cdot\sqrt{294}\)
5. \(-\frac{\sqrt{28}}{\sqrt{7}}\)
6. \(\frac{\sqrt{48}}{\sqrt{3}}\)
7. \(-\frac{\sqrt{450}}{\sqrt{2}}\)
8. \(\frac{\sqrt{2890}}{\sqrt{10}}\)
9. \(\sqrt{2}\cdot\sqrt{98}\)
10. \(\frac{\sqrt{768}}{\sqrt{3}}\)
11. \(-\frac{\sqrt{3610}}{\sqrt{10}}\)
12. \(\sqrt{2}\cdot\sqrt{162}\)

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Verbetersleutel

1. \(-\frac{\sqrt{12}}{\sqrt{3}}=-\sqrt{ \frac{12}{3}}=-\sqrt{ 4}=-2\)
2. \(\sqrt{3}\cdot\sqrt{192}=\sqrt{3 \cdot 192}=\sqrt{3 \cdot 3 \cdot 64}=\sqrt{3 \cdot 3} \cdot \sqrt{64}=3\cdot8=24\)
3. \(-\sqrt{5}\cdot\sqrt{605}=-\sqrt{5 \cdot 605}=-\sqrt{5 \cdot 5 \cdot 121}=-\sqrt{5 \cdot 5} \cdot \sqrt{121}=-5\cdot11=-55\)
4. \(-\sqrt{6}\cdot\sqrt{294}=-\sqrt{6 \cdot 294}=-\sqrt{6 \cdot 6 \cdot 49}=-\sqrt{6 \cdot 6} \cdot \sqrt{49}=-6\cdot7=-42\)
5. \(-\frac{\sqrt{28}}{\sqrt{7}}=-\sqrt{ \frac{28}{7}}=-\sqrt{ 4}=-2\)
6. \(\frac{\sqrt{48}}{\sqrt{3}}=\sqrt{ \frac{48}{3}}=\sqrt{ 16}=4\)
7. \(-\frac{\sqrt{450}}{\sqrt{2}}=-\sqrt{ \frac{450}{2}}=-\sqrt{ 225}=-15\)
8. \(\frac{\sqrt{2890}}{\sqrt{10}}=\sqrt{ \frac{2890}{10}}=\sqrt{ 289}=17\)
9. \(\sqrt{2}\cdot\sqrt{98}=\sqrt{2 \cdot 98}=\sqrt{2 \cdot 2 \cdot 49}=\sqrt{2 \cdot 2} \cdot \sqrt{49}=2\cdot7=14\)
10. \(\frac{\sqrt{768}}{\sqrt{3}}=\sqrt{ \frac{768}{3}}=\sqrt{ 256}=16\)
11. \(-\frac{\sqrt{3610}}{\sqrt{10}}=-\sqrt{ \frac{3610}{10}}=-\sqrt{ 361}=-19\)
12. \(\sqrt{2}\cdot\sqrt{162}=\sqrt{2 \cdot 162}=\sqrt{2 \cdot 2 \cdot 81}=\sqrt{2 \cdot 2} \cdot \sqrt{81}=2\cdot9=18\)