Simplify square root of 25x^4y^3

$\sqrt{25 x^{4} y^{3}}$

Step 1

Rewrite $25 x^{4} y^{3}$ as ${(5 x^{2} y)}^{2} y$ .

Rewrite $25$ as $5^{2}$ .

$\sqrt{5^{2} x^{4} y^{3}}$

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

$\sqrt{5^{2} {(x^{2})}^{2} y^{3}}$

Factor out $y^{2}$ .

$\sqrt{5^{2} {(x^{2})}^{2} (y^{2} y)}$

Rewrite $5^{2} {(x^{2})}^{2} y^{2}$ as ${(5 x^{2} y)}^{2}$ .

$\sqrt{{(5 x^{2} y)}^{2} y}$

Step 2

Pull terms out from under the radical.

$5 x^{2} y \sqrt{y}$