Simplify square root of 16x^4y^3

$\sqrt{16 x^{4} y^{3}}$

Step 1

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

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

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

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

$\sqrt{4^{2} {(x^{2})}^{2} y^{3}}$

Factor out $y^{2}$ .

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

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

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

Step 2

Pull terms out from under the radical.

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