Rekenen met wortels (reeks 3)

Hoofdmenu Eentje per keer  🖨

Reken uit

1. \(-\sqrt{5}\cdot\sqrt{605}\)
2. \(-\sqrt{3}\cdot\sqrt{12}\)
3. \(\frac{\sqrt{4212}}{\sqrt{13}}\)
4. \(-\sqrt{2}\cdot\sqrt{50}\)
5. \(-\frac{\sqrt{1690}}{\sqrt{10}}\)
6. \(-\sqrt{10}\cdot\sqrt{490}\)
7. \(\frac{\sqrt{1734}}{\sqrt{6}}\)
8. \(-\sqrt{10}\cdot\sqrt{1210}\)
9. \(-\frac{\sqrt{1083}}{\sqrt{3}}\)
10. \(-\sqrt{5}\cdot\sqrt{245}\)
11. \(\sqrt{3}\cdot\sqrt{147}\)
12. \(\frac{\sqrt{192}}{\sqrt{3}}\)

---

Reken uit

Verbetersleutel

1. \(-\sqrt{5}\cdot\sqrt{605}=-\sqrt{5 \cdot 605}=-\sqrt{5 \cdot 5 \cdot 121}=-\sqrt{5 \cdot 5} \cdot \sqrt{121}=-5\cdot11=-55\)
2. \(-\sqrt{3}\cdot\sqrt{12}=-\sqrt{3 \cdot 12}=-\sqrt{3 \cdot 3 \cdot 4}=-\sqrt{3 \cdot 3} \cdot \sqrt{4}=-3\cdot2=-6\)
3. \(\frac{\sqrt{4212}}{\sqrt{13}}=\sqrt{ \frac{4212}{13}}=\sqrt{ 324}=18\)
4. \(-\sqrt{2}\cdot\sqrt{50}=-\sqrt{2 \cdot 50}=-\sqrt{2 \cdot 2 \cdot 25}=-\sqrt{2 \cdot 2} \cdot \sqrt{25}=-2\cdot5=-10\)
5. \(-\frac{\sqrt{1690}}{\sqrt{10}}=-\sqrt{ \frac{1690}{10}}=-\sqrt{ 169}=-13\)
6. \(-\sqrt{10}\cdot\sqrt{490}=-\sqrt{10 \cdot 490}=-\sqrt{10 \cdot 10 \cdot 49}=-\sqrt{10 \cdot 10} \cdot \sqrt{49}=-10\cdot7=-70\)
7. \(\frac{\sqrt{1734}}{\sqrt{6}}=\sqrt{ \frac{1734}{6}}=\sqrt{ 289}=17\)
8. \(-\sqrt{10}\cdot\sqrt{1210}=-\sqrt{10 \cdot 1210}=-\sqrt{10 \cdot 10 \cdot 121}=-\sqrt{10 \cdot 10} \cdot \sqrt{121}=-10\cdot11=-110\)
9. \(-\frac{\sqrt{1083}}{\sqrt{3}}=-\sqrt{ \frac{1083}{3}}=-\sqrt{ 361}=-19\)
10. \(-\sqrt{5}\cdot\sqrt{245}=-\sqrt{5 \cdot 245}=-\sqrt{5 \cdot 5 \cdot 49}=-\sqrt{5 \cdot 5} \cdot \sqrt{49}=-5\cdot7=-35\)
11. \(\sqrt{3}\cdot\sqrt{147}=\sqrt{3 \cdot 147}=\sqrt{3 \cdot 3 \cdot 49}=\sqrt{3 \cdot 3} \cdot \sqrt{49}=3\cdot7=21\)
12. \(\frac{\sqrt{192}}{\sqrt{3}}=\sqrt{ \frac{192}{3}}=\sqrt{ 64}=8\)