Simplify square root of 3x^18y

$\sqrt{3 x^{18} y}$

Step 1

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

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

$\sqrt{3 {(x^{9})}^{2} y}$

Reorder $3$ and ${(x^{9})}^{2}$ .

$\sqrt{{(x^{9})}^{2} \cdot 3 y}$

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

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

Add parentheses.

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

Step 2

Pull terms out from under the radical.

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

Step 3

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

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