Problem

$\sqrt{(x-4)^{3}}-125=0$

Answer

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Answer

\(\boxed{x=29}\)

Steps

Step 1 ：\(\sqrt{(x-4)^{3}}-125=0\)

Step 2 ：\(\sqrt{(x-4)^{3}}=125\)

Step 3 ：\((x-4)^{3}=125^2\)

Step 4 ：\(x-4=\sqrt[3]{125^2}\)

Step 5 ：\(x=\sqrt[3]{125^2}+4\)

Step 6 ：\(\boxed{x=29}\)

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