Simplify square root of (11n^2)/(9m^2)

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

Step 1

Rewrite $\frac{11 n^{2}}{9 m^{2}}$ as ${(\frac{n}{3 m})}^{2} \cdot 11$ .

Factor the perfect power $n^{2}$ out of $11 n^{2}$ .

$\sqrt{\frac{n^{2} \cdot 11}{9 m^{2}}}$

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

$\sqrt{\frac{n^{2} \cdot 11}{{(3 m)}^{2} \cdot 1}}$

Rearrange the fraction $\frac{n^{2} \cdot 11}{{(3 m)}^{2} \cdot 1}$ .

$\sqrt{{(\frac{n}{3 m})}^{2} \cdot 11}$

Step 2

Pull terms out from under the radical.

$\frac{n}{3 m} \sqrt{11}$

Step 3

Combine $\frac{n}{3 m}$ and $\sqrt{11}$ .

$\frac{n \sqrt{11}}{3 m}$