4. Найдите значение выражения (√3 ⁶/₇ - √1 ⁵/₇) : √3/28

4. Найдем значение выражения:

$$(\sqrt{3\frac{6}{7}} - \sqrt{1\frac{5}{7}}) : \sqrt{\frac{3}{28}} = (\sqrt{\frac{27}{7}} - \sqrt{\frac{12}{7}}) : \sqrt{\frac{3}{28}} = (\frac{\sqrt{27}}{\sqrt{7}} - \frac{\sqrt{12}}{\sqrt{7}}) : \frac{\sqrt{3}}{\sqrt{28}} = \frac{\sqrt{27} - \sqrt{12}}{\sqrt{7}} : \frac{\sqrt{3}}{2\sqrt{7}} = \frac{2\sqrt{7}}{\sqrt{7}} \cdot \frac{\sqrt{27} - \sqrt{12}}{\sqrt{3}} = 2(\frac{\sqrt{27}}{\sqrt{3}} - \frac{\sqrt{12}}{\sqrt{3}}) = 2(\sqrt{\frac{27}{3}} - \sqrt{\frac{12}{3}}) = 2(\sqrt{9} - \sqrt{4}) = 2(3-2) = 2 \cdot 1 = 2$$

Ответ: 2