Rekenen met wortels (reeks 3)

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1. \(\sqrt{2}\cdot\sqrt{50}\)
2. \(-\sqrt{10}\cdot\sqrt{490}\)
3. \(\sqrt{10}\cdot\sqrt{810}\)
4. \(-\frac{\sqrt{1792}}{\sqrt{7}}\)
5. \(\frac{\sqrt{1014}}{\sqrt{6}}\)
6. \(\frac{\sqrt{578}}{\sqrt{2}}\)
7. \(\sqrt{10}\cdot\sqrt{1210}\)
8. \(-\frac{\sqrt{192}}{\sqrt{3}}\)
9. \(\frac{\sqrt{2800}}{\sqrt{7}}\)
10. \(\sqrt{5}\cdot\sqrt{80}\)
11. \(\frac{\sqrt{5200}}{\sqrt{13}}\)
12. \(-\sqrt{5}\cdot\sqrt{20}\)

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Verbetersleutel

1. \(\sqrt{2}\cdot\sqrt{50}=\sqrt{2 \cdot 50}=\sqrt{2 \cdot 2 \cdot 25}=\sqrt{2 \cdot 2} \cdot \sqrt{25}=2\cdot5=10\)
2. \(-\sqrt{10}\cdot\sqrt{490}=-\sqrt{10 \cdot 490}=-\sqrt{10 \cdot 10 \cdot 49}=-\sqrt{10 \cdot 10} \cdot \sqrt{49}=-10\cdot7=-70\)
3. \(\sqrt{10}\cdot\sqrt{810}=\sqrt{10 \cdot 810}=\sqrt{10 \cdot 10 \cdot 81}=\sqrt{10 \cdot 10} \cdot \sqrt{81}=10\cdot9=90\)
4. \(-\frac{\sqrt{1792}}{\sqrt{7}}=-\sqrt{ \frac{1792}{7}}=-\sqrt{ 256}=-16\)
5. \(\frac{\sqrt{1014}}{\sqrt{6}}=\sqrt{ \frac{1014}{6}}=\sqrt{ 169}=13\)
6. \(\frac{\sqrt{578}}{\sqrt{2}}=\sqrt{ \frac{578}{2}}=\sqrt{ 289}=17\)
7. \(\sqrt{10}\cdot\sqrt{1210}=\sqrt{10 \cdot 1210}=\sqrt{10 \cdot 10 \cdot 121}=\sqrt{10 \cdot 10} \cdot \sqrt{121}=10\cdot11=110\)
8. \(-\frac{\sqrt{192}}{\sqrt{3}}=-\sqrt{ \frac{192}{3}}=-\sqrt{ 64}=-8\)
9. \(\frac{\sqrt{2800}}{\sqrt{7}}=\sqrt{ \frac{2800}{7}}=\sqrt{ 400}=20\)
10. \(\sqrt{5}\cdot\sqrt{80}=\sqrt{5 \cdot 80}=\sqrt{5 \cdot 5 \cdot 16}=\sqrt{5 \cdot 5} \cdot \sqrt{16}=5\cdot4=20\)
11. \(\frac{\sqrt{5200}}{\sqrt{13}}=\sqrt{ \frac{5200}{13}}=\sqrt{ 400}=20\)
12. \(-\sqrt{5}\cdot\sqrt{20}=-\sqrt{5 \cdot 20}=-\sqrt{5 \cdot 5 \cdot 4}=-\sqrt{5 \cdot 5} \cdot \sqrt{4}=-5\cdot2=-10\)