4. Вычислите: $$(5\frac{5}{6} + 1\frac{2}{3})^2 \cdot \frac{4}{5}$$.

4. Вычислите: $$(5\frac{5}{6} + 1\frac{2}{3})^2 \cdot \frac{4}{5}$$

$$(5\frac{5}{6} + 1\frac{2}{3})^2 \cdot \frac{4}{5} = (\frac{5 \cdot 6 + 5}{6} + \frac{1 \cdot 3 + 2}{3})^2 \cdot \frac{4}{5} = (\frac{35}{6} + \frac{5}{3})^2 \cdot \frac{4}{5} = (\frac{35}{6} + \frac{5 \cdot 2}{3 \cdot 2})^2 \cdot \frac{4}{5} = (\frac{35}{6} + \frac{10}{6})^2 \cdot \frac{4}{5} = (\frac{35 + 10}{6})^2 \cdot \frac{4}{5} = (\frac{45}{6})^2 \cdot \frac{4}{5} = (\frac{15}{2})^2 \cdot \frac{4}{5} = \frac{225}{4} \cdot \frac{4}{5} = \frac{225 \cdot 4}{4 \cdot 5} = \frac{225}{5} = 45$$

Ответ: 45