Simplify square root of 11xy^18

$\sqrt{11 x y^{18}}$

Step 1

Rewrite $11 x y^{18}$ as ${(y^{3^{2}})}^{2} \cdot (11 x)$ .

Rewrite $y^{18}$ as ${(y^{9})}^{2}$ .

$\sqrt{11 x {(y^{9})}^{2}}$

Move $x$ .

$\sqrt{11 {(y^{9})}^{2} x}$

Reorder $11$ and ${(y^{9})}^{2}$ .

$\sqrt{{(y^{9})}^{2} \cdot 11 x}$

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

$\sqrt{{(y^{3^{2}})}^{2} \cdot 11 x}$

Add parentheses.

$\sqrt{{(y^{3^{2}})}^{2} \cdot (11 x)}$

Step 2

Pull terms out from under the radical.

$y^{3^{2}} \sqrt{11 x}$

Step 3

Raise $3$ to the power of $2$ .

$y^{9} \sqrt{11 x}$