Simplify square root of 32x

$\sqrt{32 x}$

Step 1

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

Factor $16$ out of $32$ .

$\sqrt{16 (2) x}$

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

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

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

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

Add parentheses.

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

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

Step 2

Pull terms out from under the radical.

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

Step 3

Raise $2$ to the power of $2$ .

$4 \sqrt{2 x}$

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