Question

Simplify:$\sqrt{\frac{125n^7}{169}\hspace{0.17em}}$

Short answer

The required answer is$\frac{5\sqrt{5}{n}^3\sqrt{n}}{13}$.

Step-by-step solution

Step 1. Given information.

The given square root is $\sqrt{\frac{125n^7}{169}}$.

Step 2. Simplify the given root.  

$\sqrt{\frac{125n^7}{169}}$
Apply radical rule.

$$\begin{gathered} \frac{\sqrt{125n^7}}{\sqrt{169}} \\ =\frac{5\sqrt{5}{n}^3\sqrt{n}}{\sqrt{169}} \\ =\frac{5\sqrt{5}{n}^3\sqrt{n}}{13} \end{gathered}$$