Simplify the Radical Expression square root of 16x^3

$\sqrt{16 x^{3}}$

Rewrite $16 x^{3}$ as ${(4 x)}^{2} x$ .

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

$\sqrt{4^{2} x^{3}}$

Factor out $x^{2}$ .

$\sqrt{4^{2} (x^{2} x)}$

Rewrite $4^{2} x^{2}$ as ${(4 x)}^{2}$ .

$\sqrt{{(4 x)}^{2} x}$

Pull terms out from under the radical.

$| 4 x | \sqrt{x}$

Remove non-negative terms from the absolute value.

$4 | x | \sqrt{x}$