Rekenen met wortels (reeks 3)

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1. \(\sqrt{5}\cdot\sqrt{405}\)
2. \(\sqrt{5}\cdot\sqrt{605}\)
3. \(\sqrt{5}\cdot\sqrt{180}\)
4. \(-\frac{\sqrt{320}}{\sqrt{5}}\)
5. \(\sqrt{3}\cdot\sqrt{192}\)
6. \(\sqrt{3}\cdot\sqrt{363}\)
7. \(\sqrt{3}\cdot\sqrt{300}\)
8. \(-\frac{\sqrt{175}}{\sqrt{7}}\)
9. \(\sqrt{6}\cdot\sqrt{294}\)
10. \(\frac{\sqrt{1445}}{\sqrt{5}}\)
11. \(-\frac{\sqrt{726}}{\sqrt{6}}\)
12. \(\sqrt{2}\cdot\sqrt{98}\)

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Verbetersleutel

1. \(\sqrt{5}\cdot\sqrt{405}=\sqrt{5 \cdot 405}=\sqrt{5 \cdot 5 \cdot 81}=\sqrt{5 \cdot 5} \cdot \sqrt{81}=5\cdot9=45\)
2. \(\sqrt{5}\cdot\sqrt{605}=\sqrt{5 \cdot 605}=\sqrt{5 \cdot 5 \cdot 121}=\sqrt{5 \cdot 5} \cdot \sqrt{121}=5\cdot11=55\)
3. \(\sqrt{5}\cdot\sqrt{180}=\sqrt{5 \cdot 180}=\sqrt{5 \cdot 5 \cdot 36}=\sqrt{5 \cdot 5} \cdot \sqrt{36}=5\cdot6=30\)
4. \(-\frac{\sqrt{320}}{\sqrt{5}}=-\sqrt{ \frac{320}{5}}=-\sqrt{ 64}=-8\)
5. \(\sqrt{3}\cdot\sqrt{192}=\sqrt{3 \cdot 192}=\sqrt{3 \cdot 3 \cdot 64}=\sqrt{3 \cdot 3} \cdot \sqrt{64}=3\cdot8=24\)
6. \(\sqrt{3}\cdot\sqrt{363}=\sqrt{3 \cdot 363}=\sqrt{3 \cdot 3 \cdot 121}=\sqrt{3 \cdot 3} \cdot \sqrt{121}=3\cdot11=33\)
7. \(\sqrt{3}\cdot\sqrt{300}=\sqrt{3 \cdot 300}=\sqrt{3 \cdot 3 \cdot 100}=\sqrt{3 \cdot 3} \cdot \sqrt{100}=3\cdot10=30\)
8. \(-\frac{\sqrt{175}}{\sqrt{7}}=-\sqrt{ \frac{175}{7}}=-\sqrt{ 25}=-5\)
9. \(\sqrt{6}\cdot\sqrt{294}=\sqrt{6 \cdot 294}=\sqrt{6 \cdot 6 \cdot 49}=\sqrt{6 \cdot 6} \cdot \sqrt{49}=6\cdot7=42\)
10. \(\frac{\sqrt{1445}}{\sqrt{5}}=\sqrt{ \frac{1445}{5}}=\sqrt{ 289}=17\)
11. \(-\frac{\sqrt{726}}{\sqrt{6}}=-\sqrt{ \frac{726}{6}}=-\sqrt{ 121}=-11\)
12. \(\sqrt{2}\cdot\sqrt{98}=\sqrt{2 \cdot 98}=\sqrt{2 \cdot 2 \cdot 49}=\sqrt{2 \cdot 2} \cdot \sqrt{49}=2\cdot7=14\)