Rekenen met wortels (reeks 3)

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1. \(\sqrt{2}\cdot\sqrt{18}\)
2. \(\frac{\sqrt{1083}}{\sqrt{3}}\)
3. \(\sqrt{6}\cdot\sqrt{294}\)
4. \(-\frac{\sqrt{180}}{\sqrt{5}}\)
5. \(\sqrt{6}\cdot\sqrt{726}\)
6. \(-\frac{\sqrt{2816}}{\sqrt{11}}\)
7. \(\frac{\sqrt{1573}}{\sqrt{13}}\)
8. \(-\frac{\sqrt{12}}{\sqrt{3}}\)
9. \(\frac{\sqrt{2156}}{\sqrt{11}}\)
10. \(\frac{\sqrt{405}}{\sqrt{5}}\)
11. \(\frac{\sqrt{1100}}{\sqrt{11}}\)
12. \(\frac{\sqrt{1300}}{\sqrt{13}}\)

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Verbetersleutel

1. \(\sqrt{2}\cdot\sqrt{18}=\sqrt{2 \cdot 18}=\sqrt{2 \cdot 2 \cdot 9}=\sqrt{2 \cdot 2} \cdot \sqrt{9}=2\cdot3=6\)
2. \(\frac{\sqrt{1083}}{\sqrt{3}}=\sqrt{ \frac{1083}{3}}=\sqrt{ 361}=19\)
3. \(\sqrt{6}\cdot\sqrt{294}=\sqrt{6 \cdot 294}=\sqrt{6 \cdot 6 \cdot 49}=\sqrt{6 \cdot 6} \cdot \sqrt{49}=6\cdot7=42\)
4. \(-\frac{\sqrt{180}}{\sqrt{5}}=-\sqrt{ \frac{180}{5}}=-\sqrt{ 36}=-6\)
5. \(\sqrt{6}\cdot\sqrt{726}=\sqrt{6 \cdot 726}=\sqrt{6 \cdot 6 \cdot 121}=\sqrt{6 \cdot 6} \cdot \sqrt{121}=6\cdot11=66\)
6. \(-\frac{\sqrt{2816}}{\sqrt{11}}=-\sqrt{ \frac{2816}{11}}=-\sqrt{ 256}=-16\)
7. \(\frac{\sqrt{1573}}{\sqrt{13}}=\sqrt{ \frac{1573}{13}}=\sqrt{ 121}=11\)
8. \(-\frac{\sqrt{12}}{\sqrt{3}}=-\sqrt{ \frac{12}{3}}=-\sqrt{ 4}=-2\)
9. \(\frac{\sqrt{2156}}{\sqrt{11}}=\sqrt{ \frac{2156}{11}}=\sqrt{ 196}=14\)
10. \(\frac{\sqrt{405}}{\sqrt{5}}=\sqrt{ \frac{405}{5}}=\sqrt{ 81}=9\)
11. \(\frac{\sqrt{1100}}{\sqrt{11}}=\sqrt{ \frac{1100}{11}}=\sqrt{ 100}=10\)
12. \(\frac{\sqrt{1300}}{\sqrt{13}}=\sqrt{ \frac{1300}{13}}=\sqrt{ 100}=10\)