395. Вычислите: a) √11⁴; б) √4⁶; в) √(-3)⁸; г) √(-6)⁴; д) √2⁸⋅3²; е) √3⁴⋅5⁶; ж) √7²⋅2⁸; з) √3⁶⋅5⁴; и) √8⁴⋅5⁶.

Question

Вопрос:

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Accepted Answer

а) $$\sqrt{11^4} = 11^{4/2} = 11^2 = \textbf{121}$$
б) $$\sqrt{4^6} = 4^{6/2} = 4^3 = \textbf{64}$$
в) $$\sqrt{(-3)^8} = ((-3)^8)^{1/2} = (-3)^4 = \textbf{81}$$
г) $$\sqrt{(-6)^4} = ((-6)^4)^{1/2} = (-6)^2 = \textbf{36}$$
д) $$\sqrt{2^8 \cdot 3^2} = \sqrt{2^8} \cdot \sqrt{3^2} = 2^{8/2} \cdot 3^{2/2} = 2^4 \cdot 3^1 = 16 \cdot 3 = \textbf{48}$$
е) $$\sqrt{3^4 \cdot 5^6} = \sqrt{3^4} \cdot \sqrt{5^6} = 3^{4/2} \cdot 5^{6/2} = 3^2 \cdot 5^3 = 9 \cdot 125 = \textbf{1125}$$
ж) $$\sqrt{7^2 \cdot 2^8} = \sqrt{7^2} \cdot \sqrt{2^8} = 7^{2/2} \cdot 2^{8/2} = 7 \cdot 2^4 = 7 \cdot 16 = \textbf{112}$$
з) $$\sqrt{3^6 \cdot 5^4} = \sqrt{3^6} \cdot \sqrt{5^4} = 3^{6/2} \cdot 5^{4/2} = 3^3 \cdot 5^2 = 27 \cdot 25 = \textbf{675}$$
и) $$\sqrt{8^4 \cdot 5^6} = \sqrt{(2^3)^4} \cdot \sqrt{5^6} = \sqrt{2^{12}} \cdot \sqrt{5^6} = 2^{12/2} \cdot 5^{6/2} = 2^6 \cdot 5^3 = 64 \cdot 125 = \textbf{8000}$$