Задание 8. Найдите значение выражения: 1 √64; 2 √56; 3 √45; 4 √93; 5 √84; 6 √36; 7 (2/10)2. 160 8 (3√5)²; 30 9 (4/2)2 64, 10 72 (2√3)2' 11 160 (2√5)2' 12 200 (5√2)2

Задание 8.

1) \[\sqrt{6^4} = 6^2 = 36\]

2) \[\sqrt{5^6} = 5^3 = 125\]

3) \[\sqrt{4^5} = \sqrt{4^4 \cdot 4} = 4^2 \sqrt{4} = 16 \cdot 2 = 32\]

4) \[\sqrt{9^3} = \sqrt{9^2 \cdot 9} = 9\sqrt{9} = 9 \cdot 3 = 27\]

5) \[\sqrt{8^4} = 8^2 = 64\]

6) \[\sqrt{3^6} = 3^3 = 27\]

7) \[\frac{(2\sqrt{10})^2}{160} = \frac{4 \cdot 10}{160} = \frac{40}{160} = \frac{1}{4} = 0.25\]

8) \[\frac{(3\sqrt{5})^2}{30} = \frac{9 \cdot 5}{30} = \frac{45}{30} = \frac{3}{2} = 1.5\]

9) \[\frac{(4\sqrt{2})^2}{64} = \frac{16 \cdot 2}{64} = \frac{32}{64} = \frac{1}{2} = 0.5\]

10) \[\frac{72}{(2\sqrt{3})^2} = \frac{72}{4 \cdot 3} = \frac{72}{12} = 6\]

11) \[\frac{160}{(2\sqrt{5})^2} = \frac{160}{4 \cdot 5} = \frac{160}{20} = 8\]

12) \[\frac{200}{(5\sqrt{2})^2} = \frac{200}{25 \cdot 2} = \frac{200}{50} = 4\]