Question

Simplify:$\sqrt{\frac{300m^5}{64}\hspace{0.17em}}$

Short answer

The required answer is$\frac{5\sqrt{3}{m}^2\sqrt{m}}{4}$.

Step-by-step solution

Step 1. Given information.

The given square root is $\sqrt{\frac{300m^5}{64}}$.

Step 2. Simplify the given root.  

$$\begin{gathered} \sqrt{\frac{300m^5}{64}} \\ =\sqrt{\frac{75m^5}{16}} \end{gathered}$$
Apply radical rule.

$$\begin{gathered} =\frac{\sqrt{75m^5}}{\sqrt{16}} \\ =\frac{5\sqrt{3}{m}^2\sqrt{m}}{\sqrt{16}} \\ =\frac{5\sqrt{3}{m}^2\sqrt{m}}{4} \end{gathered}$$