Question

How do you find the square root of $-63$ ?

Answer 1

Finding the square root of a negative number.

The square root of $-63$ can be calculated as follows:

$$\begin{gathered} \sqrt{-63}=\sqrt{63}·\sqrt{-1} \\ \Rightarrow \sqrt{-63}=\sqrt{3·3·7}·i[\because i=\sqrt{-1}] \\ \Rightarrow \sqrt{-63}=3\sqrt{7}i \end{gathered}$$

Here, the square root of $-1$ is denoted by $i$.

Therefore, the square root of $\mathbf{-}\mathbf{63}$ is $\mathbf{3}\sqrt{\mathbf{7}}\mathit{i}$.