Rekenen met wortels (reeks 3)

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1. \(\frac{\sqrt{98}}{\sqrt{2}}\)
2. \(-\sqrt{10}\cdot\sqrt{1210}\)
3. \(\frac{\sqrt{726}}{\sqrt{6}}\)
4. \(\sqrt{10}\cdot\sqrt{490}\)
5. \(-\frac{\sqrt{48}}{\sqrt{3}}\)
6. \(-\sqrt{10}\cdot\sqrt{810}\)
7. \(-\frac{\sqrt{405}}{\sqrt{5}}\)
8. \(-\sqrt{10}\cdot\sqrt{90}\)
9. \(-\sqrt{3}\cdot\sqrt{12}\)
10. \(-\frac{\sqrt{117}}{\sqrt{13}}\)
11. \(-\sqrt{2}\cdot\sqrt{18}\)
12. \(\frac{\sqrt{180}}{\sqrt{5}}\)

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Verbetersleutel

1. \(\frac{\sqrt{98}}{\sqrt{2}}=\sqrt{ \frac{98}{2}}=\sqrt{ 49}=7\)
2. \(-\sqrt{10}\cdot\sqrt{1210}=-\sqrt{10 \cdot 1210}=-\sqrt{10 \cdot 10 \cdot 121}=-\sqrt{10 \cdot 10} \cdot \sqrt{121}=-10\cdot11=-110\)
3. \(\frac{\sqrt{726}}{\sqrt{6}}=\sqrt{ \frac{726}{6}}=\sqrt{ 121}=11\)
4. \(\sqrt{10}\cdot\sqrt{490}=\sqrt{10 \cdot 490}=\sqrt{10 \cdot 10 \cdot 49}=\sqrt{10 \cdot 10} \cdot \sqrt{49}=10\cdot7=70\)
5. \(-\frac{\sqrt{48}}{\sqrt{3}}=-\sqrt{ \frac{48}{3}}=-\sqrt{ 16}=-4\)
6. \(-\sqrt{10}\cdot\sqrt{810}=-\sqrt{10 \cdot 810}=-\sqrt{10 \cdot 10 \cdot 81}=-\sqrt{10 \cdot 10} \cdot \sqrt{81}=-10\cdot9=-90\)
7. \(-\frac{\sqrt{405}}{\sqrt{5}}=-\sqrt{ \frac{405}{5}}=-\sqrt{ 81}=-9\)
8. \(-\sqrt{10}\cdot\sqrt{90}=-\sqrt{10 \cdot 90}=-\sqrt{10 \cdot 10 \cdot 9}=-\sqrt{10 \cdot 10} \cdot \sqrt{9}=-10\cdot3=-30\)
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. \(-\frac{\sqrt{117}}{\sqrt{13}}=-\sqrt{ \frac{117}{13}}=-\sqrt{ 9}=-3\)
11. \(-\sqrt{2}\cdot\sqrt{18}=-\sqrt{2 \cdot 18}=-\sqrt{2 \cdot 2 \cdot 9}=-\sqrt{2 \cdot 2} \cdot \sqrt{9}=-2\cdot3=-6\)
12. \(\frac{\sqrt{180}}{\sqrt{5}}=\sqrt{ \frac{180}{5}}=\sqrt{ 36}=6\)