Simplify square root of 54x^9y^7

$\sqrt{54 x^{9} y^{7}}$

Step 1

Rewrite $54 x^{9} y^{7}$ as ${(3 x^{4} y^{3})}^{2} \cdot (6 x y)$ .

Factor $9$ out of $54$ .

$\sqrt{9 (6) x^{9} y^{7}}$

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

$\sqrt{3^{2} \cdot 6 x^{9} y^{7}}$

Factor out $x^{8}$ .

$\sqrt{3^{2} \cdot 6 (x^{8} x) y^{7}}$

Rewrite $x^{8}$ as ${(x^{4})}^{2}$ .

$\sqrt{3^{2} \cdot 6 ({(x^{4})}^{2} x) y^{7}}$

Factor out $y^{6}$ .

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

Rewrite $y^{6}$ as ${(y^{3})}^{2}$ .

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

Move $x$ .

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

Move $6$ .

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

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

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

Add parentheses.

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

Add parentheses.

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

Step 2

Pull terms out from under the radical.

$3 x^{4} y^{3} \sqrt{6 x y}$