Simplify square root of 18x^5y^6

$\sqrt{18 x^{5} y^{6}}$

Step 1

Rewrite $18 x^{5} y^{6}$ as ${(3 x^{2} y^{3})}^{2} \cdot (2 x)$ .

Factor $9$ out of $18$ .

$\sqrt{9 (2) x^{5} y^{6}}$

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

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

Factor out $x^{4}$ .

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

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

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

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

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

Move $x$ .

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

Move $2$ .

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

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

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

Add parentheses.

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

Step 2

Pull terms out from under the radical.

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