Simplify square root of 45/(4m^4)

$\sqrt{\frac{45}{4 m^{4}}}$

Step 1

Rewrite $\frac{45}{4 m^{4}}$ as ${(\frac{3}{2 m^{2}})}^{2} \cdot 5$ .

Factor the perfect power $3^{2}$ out of $45$ .

$\sqrt{\frac{3^{2} \cdot 5}{4 m^{4}}}$

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

$\sqrt{\frac{3^{2} \cdot 5}{{(2 m^{2})}^{2} \cdot 1}}$

Rearrange the fraction $\frac{3^{2} \cdot 5}{{(2 m^{2})}^{2} \cdot 1}$ .

$\sqrt{{(\frac{3}{2 m^{2}})}^{2} \cdot 5}$

Step 2

Pull terms out from under the radical.

$\frac{3}{2 m^{2}} \sqrt{5}$

Step 3

Combine $\frac{3}{2 m^{2}}$ and $\sqrt{5}$ .

$\frac{3 \sqrt{5}}{2 m^{2}}$