Simplify square root of (8x^3y^5)/(2xy^2)

$\sqrt{\frac{8 x^{3} y^{5}}{2 x y^{2}}}$

Reduce the expression $\frac{8 x^{3} y^{5}}{2 x y^{2}}$ by cancelling the common factors.

Factor $2$ out of $8 x^{3} y^{5}$ .

$\sqrt{\frac{2 (4 x^{3} y^{5})}{2 x y^{2}}}$

Factor $2$ out of $2 x y^{2}$ .

$\sqrt{\frac{2 (4 x^{3} y^{5})}{2 (x y^{2})}}$

Cancel the common factor.

$\sqrt{\frac{2 (4 x^{3} y^{5})}{2 (x y^{2})}}$

Rewrite the expression.

$\sqrt{\frac{4 x^{3} y^{5}}{x y^{2}}}$

Cancel the common factor of $x^{3}$ and $x$ .

Factor $x$ out of $4 x^{3} y^{5}$ .

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

Cancel the common factors.

Factor $x$ out of $x y^{2}$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $y^{5}$ and $y^{2}$ .

Factor $y^{2}$ out of $4 x^{2} y^{5}$ .

$\sqrt{\frac{y^{2} (4 x^{2} y^{3})}{y^{2}}}$

Cancel the common factors.

Multiply by $1$ .

$\sqrt{\frac{y^{2} (4 x^{2} y^{3})}{y^{2} \cdot 1}}$

Cancel the common factor.

$\sqrt{\frac{y^{2} (4 x^{2} y^{3})}{y^{2} \cdot 1}}$

Rewrite the expression.

$\sqrt{\frac{4 x^{2} y^{3}}{1}}$

Divide $4 x^{2} y^{3}$ by $1$ .

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

Rewrite $4 x^{2} y^{3}$ as ${(2 x y)}^{2} y$ .

Rewrite $4$ as $2^{2}$ .

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

Factor out $y^{2}$ .

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

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

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

Pull terms out from under the radical.

$2 x y \sqrt{y}$