Simplify the Radical Expression square root of (224x^9)/(36y^10)

$\sqrt{\frac{224 x^{9}}{36 y^{10}}}$

Reduce the expression $\frac{224 x^{9}}{36 y^{10}}$ by cancelling the common factors.

Factor $4$ out of $224 x^{9}$ .

$\sqrt{\frac{4 (56 x^{9})}{36 y^{10}}}$

Factor $4$ out of $36 y^{10}$ .

$\sqrt{\frac{4 (56 x^{9})}{4 (9 y^{10})}}$

Cancel the common factor.

$\sqrt{\frac{4 (56 x^{9})}{4 (9 y^{10})}}$

Rewrite the expression.

$\sqrt{\frac{56 x^{9}}{9 y^{10}}}$

Rewrite $\frac{56 x^{9}}{9 y^{10}}$ as ${(\frac{2 x^{4}}{3 y^{5}})}^{2} (14 x)$ .

Factor the perfect power ${(2 x^{4})}^{2}$ out of $56 x^{9}$ .

$\sqrt{\frac{{(2 x^{4})}^{2} \cdot (14 x)}{9 y^{10}}}$

Factor the perfect power ${(3 y^{5})}^{2}$ out of $9 y^{10}$ .

$\sqrt{\frac{{(2 x^{4})}^{2} \cdot (14 x)}{{(3 y^{5})}^{2} \cdot 1}}$

Rearrange the fraction $\frac{{(2 x^{4})}^{2} \cdot (14 x)}{{(3 y^{5})}^{2} \cdot 1}$ .

$\sqrt{{(\frac{2 x^{4}}{3 y^{5}})}^{2} (14 x)}$

Pull terms out from under the radical.

$| \frac{2 x^{4}}{3 y^{5}} | \sqrt{14 x}$

Remove non-negative terms from the absolute value.

$\frac{2 x^{4}}{3 | y^{5} |} \sqrt{14 x}$

Combine $\frac{2 x^{4}}{3 | y^{5} |}$ and $\sqrt{14 x}$ .

$\frac{2 x^{4} \sqrt{14 x}}{3 | y^{5} |}$