Simplify square root of (24x^6y)/(128x^4y^5)

$\sqrt{\frac{24 x^{6} y}{128 x^{4} y^{5}}}$

Reduce the expression $\frac{24 x^{6} y}{128 x^{4} y^{5}}$ by cancelling the common factors.

Factor $8$ out of $24 x^{6} y$ .

$\sqrt{\frac{8 (3 x^{6} y)}{128 x^{4} y^{5}}}$

Factor $8$ out of $128 x^{4} y^{5}$ .

$\sqrt{\frac{8 (3 x^{6} y)}{8 (16 x^{4} y^{5})}}$

Cancel the common factor.

$\sqrt{\frac{8 (3 x^{6} y)}{8 (16 x^{4} y^{5})}}$

Rewrite the expression.

$\sqrt{\frac{3 x^{6} y}{16 x^{4} y^{5}}}$

Cancel the common factor of $x^{6}$ and $x^{4}$ .

Factor $x^{4}$ out of $3 x^{6} y$ .

$\sqrt{\frac{x^{4} (3 x^{2} y)}{16 x^{4} y^{5}}}$

Cancel the common factors.

Factor $x^{4}$ out of $16 x^{4} y^{5}$ .

$\sqrt{\frac{x^{4} (3 x^{2} y)}{x^{4} (16 y^{5})}}$

Cancel the common factor.

$\sqrt{\frac{x^{4} (3 x^{2} y)}{x^{4} (16 y^{5})}}$

Rewrite the expression.

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

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

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

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

Cancel the common factors.

Factor $y$ out of $16 y^{5}$ .

$\sqrt{\frac{y (3 x^{2})}{y (16 y^{4})}}$

Cancel the common factor.

$\sqrt{\frac{y (3 x^{2})}{y (16 y^{4})}}$

Rewrite the expression.

$\sqrt{\frac{3 x^{2}}{16 y^{4}}}$

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

Factor the perfect power $x^{2}$ out of $3 x^{2}$ .

$\sqrt{\frac{x^{2} \cdot 3}{16 y^{4}}}$

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

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

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

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

Pull terms out from under the radical.

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

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

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