Simplify the Radical Expression square root of (416u^11)/(484v^6)

$\sqrt{\frac{416 u^{11}}{484 v^{6}}}$

Step 1

Reduce the expression $\frac{416 u^{11}}{484 v^{6}}$ by cancelling the common factors.

Factor $4$ out of $416 u^{11}$ .

$\sqrt{\frac{4 (104 u^{11})}{484 v^{6}}}$

Factor $4$ out of $484 v^{6}$ .

$\sqrt{\frac{4 (104 u^{11})}{4 (121 v^{6})}}$

Cancel the common factor.

$\sqrt{\frac{4 (104 u^{11})}{4 (121 v^{6})}}$

Rewrite the expression.

$\sqrt{\frac{104 u^{11}}{121 v^{6}}}$

Step 2

Rewrite $\frac{104 u^{11}}{121 v^{6}}$ as ${(\frac{2 u^{5}}{11 v^{3}})}^{2} (26 u)$ .

Factor the perfect power ${(2 u^{5})}^{2}$ out of $104 u^{11}$ .

$\sqrt{\frac{{(2 u^{5})}^{2} \cdot (26 u)}{121 v^{6}}}$

Factor the perfect power ${(11 v^{3})}^{2}$ out of $121 v^{6}$ .

$\sqrt{\frac{{(2 u^{5})}^{2} \cdot (26 u)}{{(11 v^{3})}^{2} \cdot 1}}$

Rearrange the fraction $\frac{{(2 u^{5})}^{2} \cdot (26 u)}{{(11 v^{3})}^{2} \cdot 1}$ .

$\sqrt{{(\frac{2 u^{5}}{11 v^{3}})}^{2} (26 u)}$

Step 3

Pull terms out from under the radical.

$| \frac{2 u^{5}}{11 v^{3}} | \sqrt{26 u}$

Step 4

Remove non-negative terms from the absolute value.

$\frac{2 | u^{5} |}{11 | v^{3} |} \sqrt{26 u}$

Step 5

Combine $\frac{2 | u^{5} |}{11 | v^{3} |}$ and $\sqrt{26 u}$ .

$\frac{2 | u^{5} | \sqrt{26 u}}{11 | v^{3} |}$