4. Найдите значение выражения: 4.1. 64 / (2√8)² 4.2. 360 / (2√10)² 4.3. 160 / (2√5)² 4.4. 220 / (2√5)² 4.5. 54 / (3√2)²

Решение:

1. \( \frac{64}{(2\sqrt{8})^2} = \frac{64}{2^2 \cdot (\sqrt{8})^2} = \frac{64}{4 \cdot 8} = \frac{64}{32} = 2 \)
2. \( \frac{360}{(2\sqrt{10})^2} = \frac{360}{2^2 \cdot (\sqrt{10})^2} = \frac{360}{4 \cdot 10} = \frac{360}{40} = 9 \)
3. \( \frac{160}{(2\sqrt{5})^2} = \frac{160}{2^2 \cdot (\sqrt{5})^2} = \frac{160}{4 \cdot 5} = \frac{160}{20} = 8 \)
4. \( \frac{220}{(2\sqrt{5})^2} = \frac{220}{2^2 \cdot (\sqrt{5})^2} = \frac{220}{4 \cdot 5} = \frac{220}{20} = 11 \)
5. \( \frac{54}{(3\sqrt{2})^2} = \frac{54}{3^2 \cdot (\sqrt{2})^2} = \frac{54}{9 \cdot 2} = \frac{54}{18} = 3 \)

Ответ: 4.1. 2, 4.2. 9, 4.3. 8, 4.4. 11, 4.5. 3.