Question

Simplify:$\sqrt{\frac{108q^{10}}{3q^2}\hspace{0.17em}}$

Short answer

The required answer is$6q^4$.

Step-by-step solution

Step 1. Given information. 

The given square root is$\sqrt{\frac{108q^{10}}{3q^2}}$.

Step 2. Simplify the given root.  

$$\begin{gathered} \sqrt{\frac{108q^{10}}{3q^2}} \\ =\sqrt{36q^8} \end{gathered}$$

Apply radical rule.

$$\begin{gathered} \sqrt{36}\sqrt{q^8} \\ =6\sqrt{q^8} \\ =6q^4 \end{gathered}$$