Simplify square root of (5n^2)/(4m^2)

$\sqrt{\frac{5 n^{2}}{4 m^{2}}}$

Step 1

Rewrite $\frac{5 n^{2}}{4 m^{2}}$ as ${(\frac{n}{2 m})}^{2} \cdot 5$ .

Factor the perfect power $n^{2}$ out of $5 n^{2}$ .

$\sqrt{\frac{n^{2} \cdot 5}{4 m^{2}}}$

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

$\sqrt{\frac{n^{2} \cdot 5}{{(2 m)}^{2} \cdot 1}}$

Rearrange the fraction $\frac{n^{2} \cdot 5}{{(2 m)}^{2} \cdot 1}$ .

$\sqrt{{(\frac{n}{2 m})}^{2} \cdot 5}$

Step 2

Pull terms out from under the radical.

$\frac{n}{2 m} \sqrt{5}$

Step 3

Combine $\frac{n}{2 m}$ and $\sqrt{5}$ .

$\frac{n \sqrt{5}}{2 m}$