Simplify square root of (126xy^5)/(32x^3)

$\sqrt{\frac{126 x y^{5}}{32 x^{3}}}$

Reduce the expression $\frac{126 x y^{5}}{32 x^{3}}$ by cancelling the common factors.

Factor $2$ out of $126 x y^{5}$ .

$\sqrt{\frac{2 (63 x y^{5})}{32 x^{3}}}$

Factor $2$ out of $32 x^{3}$ .

$\sqrt{\frac{2 (63 x y^{5})}{2 (16 x^{3})}}$

Cancel the common factor.

$\sqrt{\frac{2 (63 x y^{5})}{2 (16 x^{3})}}$

Rewrite the expression.

$\sqrt{\frac{63 x y^{5}}{16 x^{3}}}$

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

Factor $x$ out of $63 x y^{5}$ .

$\sqrt{\frac{x (63 y^{5})}{16 x^{3}}}$

Cancel the common factors.

Factor $x$ out of $16 x^{3}$ .

$\sqrt{\frac{x (63 y^{5})}{x (16 x^{2})}}$

Cancel the common factor.

$\sqrt{\frac{x (63 y^{5})}{x (16 x^{2})}}$

Rewrite the expression.

$\sqrt{\frac{63 y^{5}}{16 x^{2}}}$

Rewrite $\frac{63 y^{5}}{16 x^{2}}$ as ${(\frac{3 y^{2}}{4 x})}^{2} (7 y)$ .

Factor the perfect power ${(3 y^{2})}^{2}$ out of $63 y^{5}$ .

$\sqrt{\frac{{(3 y^{2})}^{2} \cdot (7 y)}{16 x^{2}}}$

Factor the perfect power ${(4 x)}^{2}$ out of $16 x^{2}$ .

$\sqrt{\frac{{(3 y^{2})}^{2} \cdot (7 y)}{{(4 x)}^{2} \cdot 1}}$

Rearrange the fraction $\frac{{(3 y^{2})}^{2} \cdot (7 y)}{{(4 x)}^{2} \cdot 1}$ .

$\sqrt{{(\frac{3 y^{2}}{4 x})}^{2} (7 y)}$

Pull terms out from under the radical.

$\frac{3 y^{2}}{4 x} \sqrt{7 y}$

Combine $\frac{3 y^{2}}{4 x}$ and $\sqrt{7 y}$ .

$\frac{3 y^{2} \sqrt{7 y}}{4 x}$