Simplify square root of 81x^3y^4

$\sqrt{81 x^{3} y^{4}}$

Step 1

Rewrite $81 x^{3} y^{4}$ as ${(9 x y^{2})}^{2} x$ .

Rewrite $81$ as $9^{2}$ .

$\sqrt{9^{2} x^{3} y^{4}}$

Factor out $x^{2}$ .

$\sqrt{9^{2} (x^{2} x) y^{4}}$

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

$\sqrt{9^{2} (x^{2} x) {(y^{2})}^{2}}$

Move $x$ .

$\sqrt{9^{2} (x^{2}) {(y^{2})}^{2} x}$

Rewrite $9^{2} (x^{2}) {(y^{2})}^{2}$ as ${(9 x y^{2})}^{2}$ .

$\sqrt{{(9 x y^{2})}^{2} x}$

Step 2

Pull terms out from under the radical.

$9 x y^{2} \sqrt{x}$