3. Найдите значение выражения: 3.1. (4√2)² / 64 3.2. (3√2)² 3.3. 180 / (2√10)² 3.4. (3√5)² / 75 3.5. (4√3)² / 60

Решение:

1. \( \frac{(4\sqrt{2})^2}{64} = \frac{4^2 \cdot (\sqrt{2})^2}{64} = \frac{16 \cdot 2}{64} = \frac{32}{64} = \frac{1}{2} \)
2. \( (3\sqrt{2})^2 = 3^2 \cdot (\sqrt{2})^2 = 9 \cdot 2 = 18 \)
3. \( \frac{180}{(2\sqrt{10})^2} = \frac{180}{2^2 \cdot (\sqrt{10})^2} = \frac{180}{4 \cdot 10} = \frac{180}{40} = \frac{18}{4} = \frac{9}{2} = 4.5 \)
4. \( \frac{(3\sqrt{5})^2}{75} = \frac{3^2 \cdot (\sqrt{5})^2}{75} = \frac{9 \cdot 5}{75} = \frac{45}{75} = \frac{3 \cdot 15}{5 \cdot 15} = \frac{3}{5} = 0.6 \)
5. \( \frac{(4\sqrt{3})^2}{60} = \frac{4^2 \cdot (\sqrt{3})^2}{60} = \frac{16 \cdot 3}{60} = \frac{48}{60} = \frac{4 \cdot 12}{5 \cdot 12} = \frac{4}{5} = 0.8 \)

Ответ: 3.1. 0.5, 3.2. 18, 3.3. 4.5, 3.4. 0.6, 3.5. 0.8.