Simplify square root of 18y^5

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

Step 1

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

Factor $9$ out of $18$ .

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

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

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

Factor out $y^{4}$ .

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

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

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

Move $2$ .

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

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

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

Add parentheses.

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

Step 2

Pull terms out from under the radical.

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