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1. \(\frac{\sqrt{539}}{\sqrt{11}}\)
2. \(\frac{\sqrt{3179}}{\sqrt{11}}\)
3. \(-\frac{\sqrt{52}}{\sqrt{13}}\)
4. \(-\sqrt{10}\cdot\sqrt{490}\)
5. \(-\sqrt{2}\cdot\sqrt{98}\)
6. \(\sqrt{3}\cdot\sqrt{192}\)
7. \(\sqrt{3}\cdot\sqrt{363}\)
8. \(\sqrt{6}\cdot\sqrt{726}\)
9. \(\sqrt{3}\cdot\sqrt{300}\)
10. \(-\frac{\sqrt{768}}{\sqrt{3}}\)
11. \(-\sqrt{5}\cdot\sqrt{20}\)
12. \(-\sqrt{3}\cdot\sqrt{12}\)

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Verbetersleutel

1. \(\frac{\sqrt{539}}{\sqrt{11}}=\sqrt{ \frac{539}{11}}=\sqrt{ 49}=7\)
2. \(\frac{\sqrt{3179}}{\sqrt{11}}=\sqrt{ \frac{3179}{11}}=\sqrt{ 289}=17\)
3. \(-\frac{\sqrt{52}}{\sqrt{13}}=-\sqrt{ \frac{52}{13}}=-\sqrt{ 4}=-2\)
4. \(-\sqrt{10}\cdot\sqrt{490}=-\sqrt{10 \cdot 490}=-\sqrt{10 \cdot 10 \cdot 49}=-\sqrt{10 \cdot 10} \cdot \sqrt{49}=-10\cdot7=-70\)
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. \(\sqrt{3}\cdot\sqrt{192}=\sqrt{3 \cdot 192}=\sqrt{3 \cdot 3 \cdot 64}=\sqrt{3 \cdot 3} \cdot \sqrt{64}=3\cdot8=24\)
7. \(\sqrt{3}\cdot\sqrt{363}=\sqrt{3 \cdot 363}=\sqrt{3 \cdot 3 \cdot 121}=\sqrt{3 \cdot 3} \cdot \sqrt{121}=3\cdot11=33\)
8. \(\sqrt{6}\cdot\sqrt{726}=\sqrt{6 \cdot 726}=\sqrt{6 \cdot 6 \cdot 121}=\sqrt{6 \cdot 6} \cdot \sqrt{121}=6\cdot11=66\)
9. \(\sqrt{3}\cdot\sqrt{300}=\sqrt{3 \cdot 300}=\sqrt{3 \cdot 3 \cdot 100}=\sqrt{3 \cdot 3} \cdot \sqrt{100}=3\cdot10=30\)
10. \(-\frac{\sqrt{768}}{\sqrt{3}}=-\sqrt{ \frac{768}{3}}=-\sqrt{ 256}=-16\)
11. \(-\sqrt{5}\cdot\sqrt{20}=-\sqrt{5 \cdot 20}=-\sqrt{5 \cdot 5 \cdot 4}=-\sqrt{5 \cdot 5} \cdot \sqrt{4}=-5\cdot2=-10\)
12. \(-\sqrt{3}\cdot\sqrt{12}=-\sqrt{3 \cdot 12}=-\sqrt{3 \cdot 3 \cdot 4}=-\sqrt{3 \cdot 3} \cdot \sqrt{4}=-3\cdot2=-6\)