Simplify square root of 90x^4y^2

$\sqrt{90 x^{4} y^{2}}$

Step 1

Rewrite $90 x^{4} y^{2}$ as ${(3 x^{2} y)}^{2} \cdot 10$ .

Factor $9$ out of $90$ .

$\sqrt{9 (10) x^{4} y^{2}}$

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

$\sqrt{3^{2} \cdot 10 x^{4} y^{2}}$

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

$\sqrt{3^{2} \cdot 10 {(x^{2})}^{2} y^{2}}$

Move $10$ .

$\sqrt{3^{2} {(x^{2})}^{2} y^{2} \cdot 10}$

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

$\sqrt{{(3 x^{2} y)}^{2} \cdot 10}$

Step 2

Pull terms out from under the radical.

$3 x^{2} y \sqrt{10}$