Simplify square root of 512x^2

$\sqrt{512 x^{2}}$

Step 1

Rewrite $512 x^{2}$ as ${(16 x)}^{2} \cdot 2$ .

Factor $256$ out of $512$ .

$\sqrt{256 (2) x^{2}}$

Rewrite $256$ as $16^{2}$ .

$\sqrt{16^{2} \cdot 2 x^{2}}$

Move $2$ .

$\sqrt{16^{2} x^{2} \cdot 2}$

Rewrite $16^{2} x^{2}$ as ${(16 x)}^{2}$ .

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

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

Step 2

Pull terms out from under the radical.

$16 x \sqrt{2}$

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