Simplify cube root of 125x^5

$\sqrt[3]{125 x^{5}}$

Step 1

Rewrite $125 x^{5}$ as ${(5 x)}^{3} x^{2}$ .

Rewrite $125$ as $5^{3}$ .

$\sqrt[3]{5^{3} x^{5}}$

Factor out $x^{3}$ .

$\sqrt[3]{5^{3} (x^{3} x^{2})}$

Rewrite $5^{3} x^{3}$ as ${(5 x)}^{3}$ .

$\sqrt[3]{{(5 x)}^{3} x^{2}}$

$\sqrt[3]{{(5 x)}^{3} x^{2}}$

Step 2

Pull terms out from under the radical.

$5 x \sqrt[3]{x^{2}}$

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