Simplify the Radical Expression square root of (348m^3n^9)/(147m^2n^11)

$\sqrt{\frac{348 m^{3} n^{9}}{147 m^{2} n^{11}}}$

Reduce the expression $\frac{348 m^{3} n^{9}}{147 m^{2} n^{11}}$ by cancelling the common factors.

Factor $3$ out of $348 m^{3} n^{9}$ .

$\sqrt{\frac{3 (116 m^{3} n^{9})}{147 m^{2} n^{11}}}$

Factor $3$ out of $147 m^{2} n^{11}$ .

$\sqrt{\frac{3 (116 m^{3} n^{9})}{3 (49 m^{2} n^{11})}}$

Cancel the common factor.

$\sqrt{\frac{3 (116 m^{3} n^{9})}{3 (49 m^{2} n^{11})}}$

Rewrite the expression.

$\sqrt{\frac{116 m^{3} n^{9}}{49 m^{2} n^{11}}}$

Cancel the common factor of $m^{3}$ and $m^{2}$ .

Factor $m^{2}$ out of $116 m^{3} n^{9}$ .

$\sqrt{\frac{m^{2} (116 m n^{9})}{49 m^{2} n^{11}}}$

Cancel the common factors.

Factor $m^{2}$ out of $49 m^{2} n^{11}$ .

$\sqrt{\frac{m^{2} (116 m n^{9})}{m^{2} (49 n^{11})}}$

Cancel the common factor.

$\sqrt{\frac{m^{2} (116 m n^{9})}{m^{2} (49 n^{11})}}$

Rewrite the expression.

$\sqrt{\frac{116 m n^{9}}{49 n^{11}}}$

Cancel the common factor of $n^{9}$ and $n^{11}$ .

Factor $n^{9}$ out of $116 m n^{9}$ .

$\sqrt{\frac{n^{9} (116 m)}{49 n^{11}}}$

Cancel the common factors.

Factor $n^{9}$ out of $49 n^{11}$ .

$\sqrt{\frac{n^{9} (116 m)}{n^{9} (49 n^{2})}}$

Cancel the common factor.

$\sqrt{\frac{n^{9} (116 m)}{n^{9} (49 n^{2})}}$

Rewrite the expression.

$\sqrt{\frac{116 m}{49 n^{2}}}$

Rewrite $\frac{116 m}{49 n^{2}}$ as ${(\frac{2}{7 n})}^{2} (29 m)$ .

Factor the perfect power $2^{2}$ out of $116 m$ .

$\sqrt{\frac{2^{2} \cdot (29 m)}{49 n^{2}}}$

Factor the perfect power ${(7 n)}^{2}$ out of $49 n^{2}$ .

$\sqrt{\frac{2^{2} \cdot (29 m)}{{(7 n)}^{2} \cdot 1}}$

Rearrange the fraction $\frac{2^{2} \cdot (29 m)}{{(7 n)}^{2} \cdot 1}$ .

$\sqrt{{(\frac{2}{7 n})}^{2} (29 m)}$

Pull terms out from under the radical.

$| \frac{2}{7 n} | \sqrt{29 m}$

Remove non-negative terms from the absolute value.

$\frac{2}{7 | n |} \sqrt{29 m}$

Combine $\frac{2}{7 | n |}$ and $\sqrt{29 m}$ .

$\frac{2 \sqrt{29 m}}{7 | n |}$