Question

Simplify:$\sqrt{\frac{200x^7}{2x^3}\hspace{0.17em}}$

Short answer

The required answer is$10x^2$.

Step-by-step solution

Step 1. Given information.

The given square root is $\sqrt{\frac{200x^7}{2x^3}}$.

Step 2. Simplify the given root.  

$$\begin{gathered} \sqrt{\frac{200x^7}{2x^3}} \\ =\sqrt{100x^4} \end{gathered}$$

Apply radical rule.

$$\begin{gathered} \sqrt{100}\sqrt{x^4} \\ =10\sqrt{x^4} \\ =10x^2 \end{gathered}$$