Simplify square root of 1350x^4y

$\sqrt{1350 x^{4} y}$

Rewrite $1350 x^{4} y$ as ${(15 x^{2})}^{2} \cdot (6 y)$ .

Factor $225$ out of $1350$ .

$\sqrt{225 (6) x^{4} y}$

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

$\sqrt{15^{2} \cdot 6 x^{4} y}$

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

$\sqrt{15^{2} \cdot 6 {(x^{2})}^{2} y}$

Move $6$ .

$\sqrt{15^{2} {(x^{2})}^{2} \cdot 6 y}$

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

$\sqrt{{(15 x^{2})}^{2} \cdot 6 y}$

Add parentheses.

$\sqrt{{(15 x^{2})}^{2} \cdot (6 y)}$

Pull terms out from under the radical.

$15 x^{2} \sqrt{6 y}$