Simplify square root of 512k^2

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

Step 1

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

Factor $256$ out of $512$ .

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

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

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

Move $2$ .

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

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

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

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

Step 2

Pull terms out from under the radical.

$16 k \sqrt{2}$

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