Simplify square root of x^5y^4

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

Step 1

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

Factor out $x^{4}$ .

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

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

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

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

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

Move $x$ .

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

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

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

Step 2

Pull terms out from under the radical.

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