8. Найдите значение выражения: 8.1. \(\frac{\sqrt{21} \cdot \sqrt{14}}{\sqrt{6}}\) 8.2. \(\frac{\sqrt{32} \cdot \sqrt{6}}{12}\)

Решение:

1. \(\frac{\sqrt{21} \cdot \sqrt{14}}{\sqrt{6}} = \frac{\sqrt{21 \cdot 14}}{\sqrt{6}} = \sqrt{\frac{21 \cdot 14}{6}} = \sqrt{\frac{3 \cdot 7 \cdot 2 \cdot 7}{2 \cdot 3}} = \sqrt{7^2} = 7\)
2. \(\frac{\sqrt{32} \cdot \sqrt{6}}{12} = \frac{\sqrt{32 \cdot 6}}{12} = \frac{\sqrt{192}}{12} = \frac{\sqrt{64 \cdot 3}}{12} = \frac{8\sqrt{3}}{12} = \frac{2\sqrt{3}}{3}\)

Ответ: 8.1. 7, 8.2. 2√3/3.