Simplify square root of 50x^2y^4

$\sqrt{50 x^{2} y^{4}}$

Step 1

Rewrite $50 x^{2} y^{4}$ as ${(5 x y^{2})}^{2} \cdot 2$ .

Factor $25$ out of $50$ .

$\sqrt{25 (2) x^{2} y^{4}}$

Rewrite $25$ as $5^{2}$ .

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

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

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

Move $2$ .

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

Rewrite $5^{2} x^{2} {(y^{2})}^{2}$ as ${(5 x y^{2})}^{2}$ .

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

Step 2

Pull terms out from under the radical.

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