Задание 8. Найдите значение выражения: 1) \(\sqrt{6^4}\); 2) \(\sqrt{5^6}\); 3) \(\sqrt{4^5}\); 4) \(\sqrt{9^3}\); 5) \(\sqrt{8^4}\); 6) \(\sqrt{3^6}\); 7) \(\frac{(2\sqrt{10})^2}{160}\); 8) \(\frac{(3\sqrt{5})^2}{30}\); 9) \(\frac{(4\sqrt{2})^2}{64}\); 10) \(\frac{72}{(2\sqrt{3})^2}\); 11) \(\frac{160}{(2\sqrt{5})^2}\); 12) \(\frac{200}{(5\sqrt{2})^2}\).

1. \(\sqrt{6^4}=6^2=36\).
2. \(\sqrt{5^6}=5^3=125\).
3. \(\sqrt{4^5}=\sqrt{1024}=32\).
4. \(\sqrt{9^3}=9\sqrt9=27\).
5. \(\sqrt{8^4}=8^2=64\).
6. \(\sqrt{3^6}=3^3=27\).
7. \(\frac{(2\sqrt{10})^2}{160}=\frac{40}{160}=\frac14\).
8. \(\frac{(3\sqrt5)^2}{30}=\frac{45}{30}=\frac32\).
9. \(\frac{(4\sqrt2)^2}{64}=\frac{32}{64}=\frac12\).
10. \(\frac{72}{(2\sqrt3)^2}=\frac{72}{12}=6\).
11. \(\frac{160}{(2\sqrt5)^2}=\frac{160}{20}=8\).
12. \(\frac{200}{(5\sqrt2)^2}=\frac{200}{50}=4\).

Ответ: 1) 36; 2) 125; 3) 32; 4) 27; 5) 64; 6) 27; 7) \(\frac14\); 8) \(\frac32\); 9) \(\frac12\); 10) 6; 11) 8; 12) 4.