Simplify square root of 1125x^4y

$\sqrt{1125 x^{4} y}$

Step 1

Rewrite $1125 x^{4} y$ as ${(15 x^{2})}^{2} \cdot (5 y)$ .

Factor $225$ out of $1125$ .

$\sqrt{225 (5) x^{4} y}$

Rewrite $225$ as $15^{2}$ .

$\sqrt{15^{2} \cdot 5 x^{4} y}$

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

$\sqrt{15^{2} \cdot 5 {(x^{2})}^{2} y}$

Move $5$ .

$\sqrt{15^{2} {(x^{2})}^{2} \cdot 5 y}$

Rewrite $15^{2} {(x^{2})}^{2}$ as ${(15 x^{2})}^{2}$ .

$\sqrt{{(15 x^{2})}^{2} \cdot 5 y}$

Add parentheses.

$\sqrt{{(15 x^{2})}^{2} \cdot (5 y)}$

Step 2

Pull terms out from under the radical.

$15 x^{2} \sqrt{5 y}$