Rekenen met wortels (reeks 3)

Hoofdmenu Eentje per keer  🖨

Reken uit

1. \(-\frac{\sqrt{75}}{\sqrt{3}}\)
2. \(\frac{\sqrt{845}}{\sqrt{5}}\)
3. \(\frac{\sqrt{2890}}{\sqrt{10}}\)
4. \(\sqrt{3}\cdot\sqrt{300}\)
5. \(-\sqrt{5}\cdot\sqrt{180}\)
6. \(-\frac{\sqrt{3757}}{\sqrt{13}}\)
7. \(-\sqrt{3}\cdot\sqrt{147}\)
8. \(-\sqrt{2}\cdot\sqrt{162}\)
9. \(-\frac{\sqrt{90}}{\sqrt{10}}\)
10. \(-\frac{\sqrt{3971}}{\sqrt{11}}\)
11. \(\sqrt{10}\cdot\sqrt{90}\)
12. \(-\sqrt{3}\cdot\sqrt{48}\)

---

Reken uit

Verbetersleutel

1. \(-\frac{\sqrt{75}}{\sqrt{3}}=-\sqrt{ \frac{75}{3}}=-\sqrt{ 25}=-5\)
2. \(\frac{\sqrt{845}}{\sqrt{5}}=\sqrt{ \frac{845}{5}}=\sqrt{ 169}=13\)
3. \(\frac{\sqrt{2890}}{\sqrt{10}}=\sqrt{ \frac{2890}{10}}=\sqrt{ 289}=17\)
4. \(\sqrt{3}\cdot\sqrt{300}=\sqrt{3 \cdot 300}=\sqrt{3 \cdot 3 \cdot 100}=\sqrt{3 \cdot 3} \cdot \sqrt{100}=3\cdot10=30\)
5. \(-\sqrt{5}\cdot\sqrt{180}=-\sqrt{5 \cdot 180}=-\sqrt{5 \cdot 5 \cdot 36}=-\sqrt{5 \cdot 5} \cdot \sqrt{36}=-5\cdot6=-30\)
6. \(-\frac{\sqrt{3757}}{\sqrt{13}}=-\sqrt{ \frac{3757}{13}}=-\sqrt{ 289}=-17\)
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. \(-\sqrt{2}\cdot\sqrt{162}=-\sqrt{2 \cdot 162}=-\sqrt{2 \cdot 2 \cdot 81}=-\sqrt{2 \cdot 2} \cdot \sqrt{81}=-2\cdot9=-18\)
9. \(-\frac{\sqrt{90}}{\sqrt{10}}=-\sqrt{ \frac{90}{10}}=-\sqrt{ 9}=-3\)
10. \(-\frac{\sqrt{3971}}{\sqrt{11}}=-\sqrt{ \frac{3971}{11}}=-\sqrt{ 361}=-19\)
11. \(\sqrt{10}\cdot\sqrt{90}=\sqrt{10 \cdot 90}=\sqrt{10 \cdot 10 \cdot 9}=\sqrt{10 \cdot 10} \cdot \sqrt{9}=10\cdot3=30\)
12. \(-\sqrt{3}\cdot\sqrt{48}=-\sqrt{3 \cdot 48}=-\sqrt{3 \cdot 3 \cdot 16}=-\sqrt{3 \cdot 3} \cdot \sqrt{16}=-3\cdot4=-12\)