Simplify square root of 54x^3y^5

$\sqrt{54 x^{3} y^{5}}$

Step 1

Rewrite $54 x^{3} y^{5}$ as ${(3 x y^{2})}^{2} \cdot (6 x y)$ .

Factor $9$ out of $54$ .

$\sqrt{9 (6) x^{3} y^{5}}$

Rewrite $9$ as $3^{2}$ .

$\sqrt{3^{2} \cdot 6 x^{3} y^{5}}$

Factor out $x^{2}$ .

$\sqrt{3^{2} \cdot 6 (x^{2} x) y^{5}}$

Factor out $y^{4}$ .

$\sqrt{3^{2} \cdot 6 (x^{2} x) (y^{4} y)}$

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

$\sqrt{3^{2} \cdot 6 (x^{2} x) ({(y^{2})}^{2} y)}$

Move $x$ .

$\sqrt{3^{2} \cdot 6 (x^{2}) {(y^{2})}^{2} x y}$

Move $6$ .

$\sqrt{3^{2} (x^{2}) {(y^{2})}^{2} \cdot 6 x y}$

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

$\sqrt{{(3 x y^{2})}^{2} \cdot 6 x y}$

Add parentheses.

$\sqrt{{(3 x y^{2})}^{2} \cdot 6 (x y)}$

Add parentheses.

$\sqrt{{(3 x y^{2})}^{2} \cdot (6 x y)}$

Step 2

Pull terms out from under the radical.

$3 x y^{2} \sqrt{6 x y}$