Question

Simplify:$\sqrt{\frac{98r^5}{100}\hspace{0.17em}}$

Short answer

The required answer is$\frac{7r^2\sqrt{r}}{5\sqrt{2}}$.

Step-by-step solution

Step 1. Given information. 

The given square root is$\sqrt{\frac{98r^5}{100}}$.

Step 2. Simplify the given root. 

$$\begin{gathered} \sqrt{\frac{98r^5}{100}} \\ =\sqrt{\frac{49r^5}{50}} \end{gathered}$$
Apply radical rule.

$$\begin{gathered} \frac{\sqrt{49r^5}}{\sqrt{50}} \\ =\frac{7r^2\sqrt{r}}{\sqrt{50}} \\ =\frac{7r^2\sqrt{r}}{5\sqrt{2}} \end{gathered}$$