Question

How do you simplify $\sqrt{-32}$?

Answer 1

Square root of complex number:

Simplify $\sqrt{-32}$.

Use the fact that the value of $\sqrt{-1}$ is equal to$i$. Then,

$$\begin{gathered} \sqrt{-32}=\sqrt{-1}.\sqrt{32} \\ =i\sqrt{32} \\ =i\sqrt{2\times 2^4} \\ =4i\sqrt{2} \end{gathered}$$

Hence the simplified form of $\sqrt{-32}$ is $4i\sqrt{2}$.