Simplify the Radical Expression square root of 512k^2

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

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

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

Pull terms out from under the radical.

$| 16 k | \sqrt{2}$

Remove non-negative terms from the absolute value.

$16 | k | \sqrt{2}$