Simplify square root of 32x^3

$\sqrt{32 x^{3}}$

Step 1

Rewrite $32 x^{3}$ as ${(4 x)}^{2} \cdot (2 x)$ .

Factor $16$ out of $32$ .

$\sqrt{16 (2) x^{3}}$

Rewrite $16$ as $4^{2}$ .

$\sqrt{4^{2} \cdot 2 x^{3}}$

Factor out $x^{2}$ .

$\sqrt{4^{2} \cdot 2 (x^{2} x)}$

Move $2$ .

$\sqrt{4^{2} x^{2} \cdot 2 x}$

Rewrite $4^{2} x^{2}$ as ${(4 x)}^{2}$ .

$\sqrt{{(4 x)}^{2} \cdot 2 x}$

Add parentheses.

$\sqrt{{(4 x)}^{2} \cdot (2 x)}$

$\sqrt{{(4 x)}^{2} \cdot (2 x)}$

Step 2

Pull terms out from under the radical.

$4 x \sqrt{2 x}$

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