Rekenen met wortels (reeks 3)

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1. \(-\frac{\sqrt{112}}{\sqrt{7}}\)
2. \(-\sqrt{10}\cdot\sqrt{90}\)
3. \(-\sqrt{3}\cdot\sqrt{300}\)
4. \(-\sqrt{3}\cdot\sqrt{147}\)
5. \(\sqrt{6}\cdot\sqrt{150}\)
6. \(-\frac{\sqrt{176}}{\sqrt{11}}\)
7. \(\sqrt{6}\cdot\sqrt{294}\)
8. \(-\frac{\sqrt{1859}}{\sqrt{11}}\)
9. \(\sqrt{3}\cdot\sqrt{12}\)
10. \(\frac{\sqrt{768}}{\sqrt{3}}\)
11. \(-\sqrt{2}\cdot\sqrt{242}\)
12. \(\sqrt{10}\cdot\sqrt{1210}\)

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Verbetersleutel

1. \(-\frac{\sqrt{112}}{\sqrt{7}}=-\sqrt{ \frac{112}{7}}=-\sqrt{ 16}=-4\)
2. \(-\sqrt{10}\cdot\sqrt{90}=-\sqrt{10 \cdot 90}=-\sqrt{10 \cdot 10 \cdot 9}=-\sqrt{10 \cdot 10} \cdot \sqrt{9}=-10\cdot3=-30\)
3. \(-\sqrt{3}\cdot\sqrt{300}=-\sqrt{3 \cdot 300}=-\sqrt{3 \cdot 3 \cdot 100}=-\sqrt{3 \cdot 3} \cdot \sqrt{100}=-3\cdot10=-30\)
4. \(-\sqrt{3}\cdot\sqrt{147}=-\sqrt{3 \cdot 147}=-\sqrt{3 \cdot 3 \cdot 49}=-\sqrt{3 \cdot 3} \cdot \sqrt{49}=-3\cdot7=-21\)
5. \(\sqrt{6}\cdot\sqrt{150}=\sqrt{6 \cdot 150}=\sqrt{6 \cdot 6 \cdot 25}=\sqrt{6 \cdot 6} \cdot \sqrt{25}=6\cdot5=30\)
6. \(-\frac{\sqrt{176}}{\sqrt{11}}=-\sqrt{ \frac{176}{11}}=-\sqrt{ 16}=-4\)
7. \(\sqrt{6}\cdot\sqrt{294}=\sqrt{6 \cdot 294}=\sqrt{6 \cdot 6 \cdot 49}=\sqrt{6 \cdot 6} \cdot \sqrt{49}=6\cdot7=42\)
8. \(-\frac{\sqrt{1859}}{\sqrt{11}}=-\sqrt{ \frac{1859}{11}}=-\sqrt{ 169}=-13\)
9. \(\sqrt{3}\cdot\sqrt{12}=\sqrt{3 \cdot 12}=\sqrt{3 \cdot 3 \cdot 4}=\sqrt{3 \cdot 3} \cdot \sqrt{4}=3\cdot2=6\)
10. \(\frac{\sqrt{768}}{\sqrt{3}}=\sqrt{ \frac{768}{3}}=\sqrt{ 256}=16\)
11. \(-\sqrt{2}\cdot\sqrt{242}=-\sqrt{2 \cdot 242}=-\sqrt{2 \cdot 2 \cdot 121}=-\sqrt{2 \cdot 2} \cdot \sqrt{121}=-2\cdot11=-22\)
12. \(\sqrt{10}\cdot\sqrt{1210}=\sqrt{10 \cdot 1210}=\sqrt{10 \cdot 10 \cdot 121}=\sqrt{10 \cdot 10} \cdot \sqrt{121}=10\cdot11=110\)