Rekenen met wortels (reeks 3)

Hoofdmenu Eentje per keer  🖨

Reken uit

1. \(-\sqrt{3}\cdot\sqrt{48}\)
2. \(\sqrt{2}\cdot\sqrt{50}\)
3. \(\sqrt{2}\cdot\sqrt{162}\)
4. \(-\sqrt{5}\cdot\sqrt{45}\)
5. \(\frac{\sqrt{704}}{\sqrt{11}}\)
6. \(-\sqrt{6}\cdot\sqrt{294}\)
7. \(\sqrt{3}\cdot\sqrt{147}\)
8. \(\frac{\sqrt{1100}}{\sqrt{11}}\)
9. \(-\frac{\sqrt{2166}}{\sqrt{6}}\)
10. \(\frac{\sqrt{192}}{\sqrt{3}}\)
11. \(-\sqrt{6}\cdot\sqrt{726}\)
12. \(-\sqrt{10}\cdot\sqrt{810}\)

---

Reken uit

Verbetersleutel

1. \(-\sqrt{3}\cdot\sqrt{48}=-\sqrt{3 \cdot 48}=-\sqrt{3 \cdot 3 \cdot 16}=-\sqrt{3 \cdot 3} \cdot \sqrt{16}=-3\cdot4=-12\)
2. \(\sqrt{2}\cdot\sqrt{50}=\sqrt{2 \cdot 50}=\sqrt{2 \cdot 2 \cdot 25}=\sqrt{2 \cdot 2} \cdot \sqrt{25}=2\cdot5=10\)
3. \(\sqrt{2}\cdot\sqrt{162}=\sqrt{2 \cdot 162}=\sqrt{2 \cdot 2 \cdot 81}=\sqrt{2 \cdot 2} \cdot \sqrt{81}=2\cdot9=18\)
4. \(-\sqrt{5}\cdot\sqrt{45}=-\sqrt{5 \cdot 45}=-\sqrt{5 \cdot 5 \cdot 9}=-\sqrt{5 \cdot 5} \cdot \sqrt{9}=-5\cdot3=-15\)
5. \(\frac{\sqrt{704}}{\sqrt{11}}=\sqrt{ \frac{704}{11}}=\sqrt{ 64}=8\)
6. \(-\sqrt{6}\cdot\sqrt{294}=-\sqrt{6 \cdot 294}=-\sqrt{6 \cdot 6 \cdot 49}=-\sqrt{6 \cdot 6} \cdot \sqrt{49}=-6\cdot7=-42\)
7. \(\sqrt{3}\cdot\sqrt{147}=\sqrt{3 \cdot 147}=\sqrt{3 \cdot 3 \cdot 49}=\sqrt{3 \cdot 3} \cdot \sqrt{49}=3\cdot7=21\)
8. \(\frac{\sqrt{1100}}{\sqrt{11}}=\sqrt{ \frac{1100}{11}}=\sqrt{ 100}=10\)
9. \(-\frac{\sqrt{2166}}{\sqrt{6}}=-\sqrt{ \frac{2166}{6}}=-\sqrt{ 361}=-19\)
10. \(\frac{\sqrt{192}}{\sqrt{3}}=\sqrt{ \frac{192}{3}}=\sqrt{ 64}=8\)
11. \(-\sqrt{6}\cdot\sqrt{726}=-\sqrt{6 \cdot 726}=-\sqrt{6 \cdot 6 \cdot 121}=-\sqrt{6 \cdot 6} \cdot \sqrt{121}=-6\cdot11=-66\)
12. \(-\sqrt{10}\cdot\sqrt{810}=-\sqrt{10 \cdot 810}=-\sqrt{10 \cdot 10 \cdot 81}=-\sqrt{10 \cdot 10} \cdot \sqrt{81}=-10\cdot9=-90\)