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) $\sqrt{0,125}=$

Answer

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Answer

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

Steps

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

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