Simplify square root of 50x^3y^5

$\sqrt{50 x^{3} y^{5}}$

Step 1

Rewrite $50 x^{3} y^{5}$ as ${(5 x y^{2})}^{2} \cdot (2 x y)$ .

Factor $25$ out of $50$ .

$\sqrt{25 (2) x^{3} y^{5}}$

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

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

Factor out $x^{2}$ .

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

Factor out $y^{4}$ .

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

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

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

Move $x$ .

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

Move $2$ .

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

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

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

Add parentheses.

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

Add parentheses.

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

Step 2

Pull terms out from under the radical.

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