Rekenen met wortels (reeks 3)

Hoofdmenu Eentje per keer  🖨

Reken uit

1. \(\sqrt{3}\cdot\sqrt{192}\)
2. \(-\frac{\sqrt{867}}{\sqrt{3}}\)
3. \(\frac{\sqrt{50}}{\sqrt{2}}\)
4. \(-\sqrt{5}\cdot\sqrt{245}\)
5. \(\sqrt{2}\cdot\sqrt{162}\)
6. \(-\sqrt{2}\cdot\sqrt{98}\)
7. \(-\sqrt{5}\cdot\sqrt{605}\)
8. \(-\sqrt{3}\cdot\sqrt{147}\)
9. \(\frac{\sqrt{605}}{\sqrt{5}}\)
10. \(-\sqrt{2}\cdot\sqrt{242}\)
11. \(-\sqrt{10}\cdot\sqrt{90}\)
12. \(-\sqrt{5}\cdot\sqrt{80}\)

---

Reken uit

Verbetersleutel

1. \(\sqrt{3}\cdot\sqrt{192}=\sqrt{3 \cdot 192}=\sqrt{3 \cdot 3 \cdot 64}=\sqrt{3 \cdot 3} \cdot \sqrt{64}=3\cdot8=24\)
2. \(-\frac{\sqrt{867}}{\sqrt{3}}=-\sqrt{ \frac{867}{3}}=-\sqrt{ 289}=-17\)
3. \(\frac{\sqrt{50}}{\sqrt{2}}=\sqrt{ \frac{50}{2}}=\sqrt{ 25}=5\)
4. \(-\sqrt{5}\cdot\sqrt{245}=-\sqrt{5 \cdot 245}=-\sqrt{5 \cdot 5 \cdot 49}=-\sqrt{5 \cdot 5} \cdot \sqrt{49}=-5\cdot7=-35\)
5. \(\sqrt{2}\cdot\sqrt{162}=\sqrt{2 \cdot 162}=\sqrt{2 \cdot 2 \cdot 81}=\sqrt{2 \cdot 2} \cdot \sqrt{81}=2\cdot9=18\)
6. \(-\sqrt{2}\cdot\sqrt{98}=-\sqrt{2 \cdot 98}=-\sqrt{2 \cdot 2 \cdot 49}=-\sqrt{2 \cdot 2} \cdot \sqrt{49}=-2\cdot7=-14\)
7. \(-\sqrt{5}\cdot\sqrt{605}=-\sqrt{5 \cdot 605}=-\sqrt{5 \cdot 5 \cdot 121}=-\sqrt{5 \cdot 5} \cdot \sqrt{121}=-5\cdot11=-55\)
8. \(-\sqrt{3}\cdot\sqrt{147}=-\sqrt{3 \cdot 147}=-\sqrt{3 \cdot 3 \cdot 49}=-\sqrt{3 \cdot 3} \cdot \sqrt{49}=-3\cdot7=-21\)
9. \(\frac{\sqrt{605}}{\sqrt{5}}=\sqrt{ \frac{605}{5}}=\sqrt{ 121}=11\)
10. \(-\sqrt{2}\cdot\sqrt{242}=-\sqrt{2 \cdot 242}=-\sqrt{2 \cdot 2 \cdot 121}=-\sqrt{2 \cdot 2} \cdot \sqrt{121}=-2\cdot11=-22\)
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. \(-\sqrt{5}\cdot\sqrt{80}=-\sqrt{5 \cdot 80}=-\sqrt{5 \cdot 5 \cdot 16}=-\sqrt{5 \cdot 5} \cdot \sqrt{16}=-5\cdot4=-20\)