Simplify square root of 512m^3

$\sqrt{512 m^{3}}$

Step 1

Rewrite $512 m^{3}$ as ${(16 m)}^{2} \cdot (2 m)$ .

Factor $256$ out of $512$ .

$\sqrt{256 (2) m^{3}}$

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

$\sqrt{16^{2} \cdot 2 m^{3}}$

Factor out $m^{2}$ .

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

Move $2$ .

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

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

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

Add parentheses.

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

Step 2

Pull terms out from under the radical.

$16 m \sqrt{2 m}$