Задание 6. Найдите значение выражения: 1 √21⋅√14 3 √22⋅√33 √8⋅√192

\[\sqrt{21} \cdot \sqrt{14} = \sqrt{3 \cdot 7} \cdot \sqrt{2 \cdot 7} = \sqrt{3 \cdot 7 \cdot 2 \cdot 7} = \sqrt{3 \cdot 2 \cdot 7^2} = 7\sqrt{6}\]

\[\sqrt{22} \cdot \sqrt{33} = \sqrt{2 \cdot 11} \cdot \sqrt{3 \cdot 11} = \sqrt{2 \cdot 11 \cdot 3 \cdot 11} = \sqrt{2 \cdot 3 \cdot 11^2} = 11\sqrt{6}\]

\[\sqrt{8} \cdot \sqrt{192} = \sqrt{2^3} \cdot \sqrt{2^6 \cdot 3} = \sqrt{2^3 \cdot 2^6 \cdot 3} = \sqrt{2^9 \cdot 3} = \sqrt{2^8 \cdot 2 \cdot 3} = 2^4\sqrt{2 \cdot 3} = 16\sqrt{6}\]