8. Найдите значение выражения $$\frac{\sqrt{51}}{\sqrt{24}} \cdot \frac{\sqrt{34}}{\sqrt{6}}$$

$$\frac{\sqrt{51}}{\sqrt{24}} \cdot \frac{\sqrt{34}}{\sqrt{6}} = \frac{\sqrt{51 \cdot 34}}{\sqrt{24 \cdot 6}} = \frac{\sqrt{3 \cdot 17 \cdot 2 \cdot 17}}{\sqrt{4 \cdot 6 \cdot 6}} = \frac{\sqrt{3 \cdot 2 \cdot 17^2}}{\sqrt{4 \cdot 6^2}} = \frac{17 \sqrt{6}}{2 \cdot 6} = \frac{17 \sqrt{6}}{12}$$ Ответ: $$\frac{17 \sqrt{6}}{12}$$