Simplify square root of 7x^18y

$\sqrt{7 x^{18} y}$

Step 1

Rewrite $7 x^{18} y$ as ${(x^{3^{2}})}^{2} \cdot (7 y)$ .

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

$\sqrt{7 {(x^{9})}^{2} y}$

Reorder $7$ and ${(x^{9})}^{2}$ .

$\sqrt{{(x^{9})}^{2} \cdot 7 y}$

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

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

Add parentheses.

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

Step 2

Pull terms out from under the radical.

$x^{3^{2}} \sqrt{7 y}$

Step 3

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

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