1. Вычислите: $\sqrt{64}$.

1. $\sqrt{64} = 8$ 2. $\sqrt{81^3} = (\sqrt{81})^3 = 9^3 = 729$ 3. $\frac{(9\sqrt{18})^2}{24} = \frac{81 \cdot 18}{24} = \frac{81 \cdot 3}{4} = 60{,}75$ 4. $\sqrt{5 \cdot 98 \cdot 10} = \sqrt{5 \cdot 49 \cdot 2 \cdot 2 \cdot 5} = \sqrt{25 \cdot 49 \cdot 4} = 5 \cdot 7 \cdot 2 = 70$ 5. $2\sqrt{32} \cdot 2\sqrt{12} \cdot \sqrt{6} = 4\sqrt{32 \cdot 12 \cdot 6} = 4\sqrt{32 \cdot 72} = 4\sqrt{2304} = 4 \cdot 48 = 192$ 6. $\frac{\sqrt{6}}{\sqrt{2 \cdot 48}} = \frac{\sqrt{6}}{\sqrt{96}} = \sqrt{\frac{6}{96}} = \sqrt{\frac{1}{16}} = 0{,}25$ 7. $(2\sqrt{5}-9)(2\sqrt{5}+9) = (2\sqrt{5})^2 - 9^2 = 20 - 81 = -61$ 8. $(\sqrt{5}-\sqrt{17})(\sqrt{5}+\sqrt{17}) = 5 - 17 = -12$ 9. $(\sqrt{5}+9)^2 - 18\sqrt{5} = (5 + 18\sqrt{5} + 81) - 18\sqrt{5} = 86$ 10. $(\sqrt{18}+\sqrt{8})\sqrt{2} = \sqrt{36}+\sqrt{16} = 6+4 = 10$ 11. $\sqrt{c^4 \cdot (-c)^{12}} = \sqrt{c^{16}} = |c^8| = 2^8 = 256$ 12. $\sqrt{\frac{u^6}{9x^4}} = \frac{|u^3|}{3x^2} = \frac{9^3}{3 \cdot 3^2} = \frac{729}{27} = 27$ 13. $\sqrt{0{,}04b^2d^4} = 0{,}2 \cdot |b| \cdot d^2 = 0{,}2 \cdot 2 \cdot 9 = 3{,}6$ 14. $\sqrt{25v^2g^4} = 5 \cdot |v| \cdot g^2 = 5 \cdot 8 \cdot 16 = 640$ 15. $\sqrt{\frac{4g^{25}}{g^{17}}} = \sqrt{4g^8} = 2g^4 = 2 \cdot 2^4 = 32$ 16. $\sqrt{\frac{1}{16}b^4n^8} = \frac{1}{4}b^2n^4 = \frac{1}{4} \cdot 25 \cdot 16 = 100$ 17. $\sqrt{9s^2 - 24sh + 16h^2} = \sqrt{(3s-4h)^2} = |3s-4h| = |3(\frac{20}{17}) - 4(\frac{202}{17})| = |\frac{60-808}{17}| = 44$ 18. $\sqrt{49v^2 + 98vx + 49x^2} = \sqrt{49(v+x)^2} = 7|v+x| = 7|7+5| = 84$ 19. $\frac{\sqrt{4b^3} \cdot \sqrt{100u}}{\sqrt{bu}} = \sqrt{\frac{4b^3 \cdot 100u}{bu}} = \sqrt{400b^2} = 20|b| = 20 \cdot 8 = 160$