Rekenen met wortels (reeks 3)

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1. \(\frac{\sqrt{2023}}{\sqrt{7}}\)
2. \(-\sqrt{10}\cdot\sqrt{90}\)
3. \(\frac{\sqrt{99}}{\sqrt{11}}\)
4. \(\sqrt{10}\cdot\sqrt{810}\)
5. \(-\sqrt{2}\cdot\sqrt{98}\)
6. \(\frac{\sqrt{2548}}{\sqrt{13}}\)
7. \(\sqrt{5}\cdot\sqrt{605}\)
8. \(\frac{\sqrt{1183}}{\sqrt{7}}\)
9. \(-\frac{\sqrt{1280}}{\sqrt{5}}\)
10. \(-\sqrt{3}\cdot\sqrt{48}\)
11. \(\sqrt{2}\cdot\sqrt{242}\)
12. \(-\frac{\sqrt{539}}{\sqrt{11}}\)

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Verbetersleutel

1. \(\frac{\sqrt{2023}}{\sqrt{7}}=\sqrt{ \frac{2023}{7}}=\sqrt{ 289}=17\)
2. \(-\sqrt{10}\cdot\sqrt{90}=-\sqrt{10 \cdot 90}=-\sqrt{10 \cdot 10 \cdot 9}=-\sqrt{10 \cdot 10} \cdot \sqrt{9}=-10\cdot3=-30\)
3. \(\frac{\sqrt{99}}{\sqrt{11}}=\sqrt{ \frac{99}{11}}=\sqrt{ 9}=3\)
4. \(\sqrt{10}\cdot\sqrt{810}=\sqrt{10 \cdot 810}=\sqrt{10 \cdot 10 \cdot 81}=\sqrt{10 \cdot 10} \cdot \sqrt{81}=10\cdot9=90\)
5. \(-\sqrt{2}\cdot\sqrt{98}=-\sqrt{2 \cdot 98}=-\sqrt{2 \cdot 2 \cdot 49}=-\sqrt{2 \cdot 2} \cdot \sqrt{49}=-2\cdot7=-14\)
6. \(\frac{\sqrt{2548}}{\sqrt{13}}=\sqrt{ \frac{2548}{13}}=\sqrt{ 196}=14\)
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. \(\frac{\sqrt{1183}}{\sqrt{7}}=\sqrt{ \frac{1183}{7}}=\sqrt{ 169}=13\)
9. \(-\frac{\sqrt{1280}}{\sqrt{5}}=-\sqrt{ \frac{1280}{5}}=-\sqrt{ 256}=-16\)
10. \(-\sqrt{3}\cdot\sqrt{48}=-\sqrt{3 \cdot 48}=-\sqrt{3 \cdot 3 \cdot 16}=-\sqrt{3 \cdot 3} \cdot \sqrt{16}=-3\cdot4=-12\)
11. \(\sqrt{2}\cdot\sqrt{242}=\sqrt{2 \cdot 242}=\sqrt{2 \cdot 2 \cdot 121}=\sqrt{2 \cdot 2} \cdot \sqrt{121}=2\cdot11=22\)
12. \(-\frac{\sqrt{539}}{\sqrt{11}}=-\sqrt{ \frac{539}{11}}=-\sqrt{ 49}=-7\)