Simplify square root of x^3y^4

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

Step 1

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

Factor out $x^{2}$ .

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

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

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

Move $x$ .

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

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

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

Step 2

Pull terms out from under the radical.

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