Прототип № 9. Найдите значение выражения: 1) \(\sqrt{51}\cdot\sqrt{12}\); 2) \(\dfrac{\sqrt{21}\cdot\sqrt{14}}{\sqrt{17}}\); 3) \(\dfrac{\sqrt{65}\cdot\sqrt{13}}{\sqrt{6}}\); 4) \(\dfrac{\sqrt{35}\cdot\sqrt{21}}{\sqrt{5}}\); 5) \(\dfrac{\sqrt{75}\cdot\sqrt{10}}{\sqrt{15}}\); 6) \(\dfrac{\sqrt{15}\cdot\sqrt{12}}{\sqrt{30}}\); 7) \(\dfrac{\sqrt{8}\cdot\sqrt{192}}{\sqrt{20}}\); 8) \(\dfrac{\sqrt{32}\cdot\sqrt{6}}{\sqrt{24}}\); 9) \(\dfrac{\sqrt{20}\cdot\sqrt{32}}{\sqrt{10}}\); 10) \(\dfrac{\sqrt{22}\cdot\sqrt{33}}{\sqrt{6}}\).

Перемножаем подкоренные числа: \(\sqrt{51\cdot12}=\sqrt{612}=6\sqrt{17}\).

Объединяем корни: \(\sqrt{\frac{21\cdot14}{17}}=\sqrt{\frac{294}{17}}=\frac{7\sqrt{102}}{17}\).

\(\sqrt{\frac{65\cdot13}{6}}=\sqrt{\frac{845}{6}}=\frac{13\sqrt{330}}{6}\).

\(\sqrt{\frac{35\cdot21}{5}}=\sqrt{147}=7\sqrt{3}\).

\(\sqrt{\frac{75\cdot10}{15}}=\sqrt{50}=5\sqrt{2}\).

\(\sqrt{\frac{15\cdot12}{30}}=\sqrt{6}\).

\(\sqrt{\frac{8\cdot192}{20}}=\sqrt{\frac{384}{5}}=\frac{8\sqrt{30}}{5}\).

\(\sqrt{\frac{32\cdot6}{24}}=\sqrt{8}=2\sqrt{2}\).

\(\sqrt{\frac{20\cdot32}{10}}=\sqrt{64}=8\).

\(\sqrt{\frac{22\cdot33}{6}}=\sqrt{121}=11\).