Rekenen met wortels (reeks 3)

Hoofdmenu Eentje per keer  🖨

Reken uit

1. \(-\sqrt{10}\cdot\sqrt{90}\)
2. \(\sqrt{2}\cdot\sqrt{242}\)
3. \(-\frac{\sqrt{704}}{\sqrt{11}}\)
4. \(-\frac{\sqrt{405}}{\sqrt{5}}\)
5. \(\frac{\sqrt{98}}{\sqrt{2}}\)
6. \(-\frac{\sqrt{80}}{\sqrt{5}}\)
7. \(-\sqrt{6}\cdot\sqrt{726}\)
8. \(\sqrt{5}\cdot\sqrt{720}\)
9. \(-\frac{\sqrt{338}}{\sqrt{2}}\)
10. \(-\frac{\sqrt{1210}}{\sqrt{10}}\)
11. \(-\frac{\sqrt{810}}{\sqrt{10}}\)
12. \(-\sqrt{5}\cdot\sqrt{320}\)

---

Reken uit

Verbetersleutel

1. \(-\sqrt{10}\cdot\sqrt{90}=-\sqrt{10 \cdot 90}=-\sqrt{10 \cdot 10 \cdot 9}=-\sqrt{10 \cdot 10} \cdot \sqrt{9}=-10\cdot3=-30\)
2. \(\sqrt{2}\cdot\sqrt{242}=\sqrt{2 \cdot 242}=\sqrt{2 \cdot 2 \cdot 121}=\sqrt{2 \cdot 2} \cdot \sqrt{121}=2\cdot11=22\)
3. \(-\frac{\sqrt{704}}{\sqrt{11}}=-\sqrt{ \frac{704}{11}}=-\sqrt{ 64}=-8\)
4. \(-\frac{\sqrt{405}}{\sqrt{5}}=-\sqrt{ \frac{405}{5}}=-\sqrt{ 81}=-9\)
5. \(\frac{\sqrt{98}}{\sqrt{2}}=\sqrt{ \frac{98}{2}}=\sqrt{ 49}=7\)
6. \(-\frac{\sqrt{80}}{\sqrt{5}}=-\sqrt{ \frac{80}{5}}=-\sqrt{ 16}=-4\)
7. \(-\sqrt{6}\cdot\sqrt{726}=-\sqrt{6 \cdot 726}=-\sqrt{6 \cdot 6 \cdot 121}=-\sqrt{6 \cdot 6} \cdot \sqrt{121}=-6\cdot11=-66\)
8. \(\sqrt{5}\cdot\sqrt{720}=\sqrt{5 \cdot 720}=\sqrt{5 \cdot 5 \cdot 144}=\sqrt{5 \cdot 5} \cdot \sqrt{144}=5\cdot12=60\)
9. \(-\frac{\sqrt{338}}{\sqrt{2}}=-\sqrt{ \frac{338}{2}}=-\sqrt{ 169}=-13\)
10. \(-\frac{\sqrt{1210}}{\sqrt{10}}=-\sqrt{ \frac{1210}{10}}=-\sqrt{ 121}=-11\)
11. \(-\frac{\sqrt{810}}{\sqrt{10}}=-\sqrt{ \frac{810}{10}}=-\sqrt{ 81}=-9\)
12. \(-\sqrt{5}\cdot\sqrt{320}=-\sqrt{5 \cdot 320}=-\sqrt{5 \cdot 5 \cdot 64}=-\sqrt{5 \cdot 5} \cdot \sqrt{64}=-5\cdot8=-40\)