Problem

a) $\sqrt{32}=$ B) $\sqrt[4]{2592}=$ c) $\sqrt{0,01}$ d) $\sqrt[3]{-125}=$ e) $\sqrt{8}=$ f) $\sqrt[3]{16}=$ G8) $\sqrt{60}$ (16) $\sqrt{200}=$ i) $\sqrt{0,125}=$

Solution

Step 1 :\(\sqrt{32}=\sqrt{2^5}=2^{\frac{5}{2}}=\boxed{4\sqrt{2}}\)

Step 2 :\(\sqrt[4]{2592}=\sqrt[4]{2^5\cdot3^4}=2^{\frac{5}{4}}\cdot3^1=\boxed{6\sqrt[4]{2}}\)

Step 3 :\(\sqrt{0.01}=\sqrt{(10^{-2})}=10^{-1}=\boxed{0.1}\)

Step 4 :\(\sqrt[3]{-125}=\sqrt[3]{(-5)^3}=\boxed{-5}\)

Step 5 :\(\sqrt{8}=\sqrt{2^3}=2^{\frac{3}{2}}=\boxed{2\sqrt{2}}\)

Step 6 :\(\sqrt[3]{16}=\sqrt[3]{2^4}=2^{\frac{4}{3}}=\boxed{2\sqrt[3]{2}}\)

Step 7 :\(\sqrt{60}=\sqrt{2^2\cdot3\cdot5}=2\sqrt{15}=\boxed{2\sqrt{15}}\)

Step 8 :\(\sqrt{200}=\sqrt{2^3\cdot5^2}=10\sqrt{2}=\boxed{10\sqrt{2}}\)

Step 9 :\(\sqrt{0.125}=\sqrt{\frac{1}{8}}=\sqrt{\frac{1}{2^3}}=\frac{1}{2^{\frac{3}{2}}}=\boxed{\frac{1}{2\sqrt{2}}}\)

From Solvely APP
Source: https://solvelyapp.com/problems/15929/

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