What is the square root of a negative number

It depends, but this is how I would do it:

Let's take the square root of -8 -->

First, I would take out an "i" and put it outside of the square root:

The i represents the negative sign. Then, I would treat the square root of 8 as a normal problem and simplify by factoring it:

Factors of 8: 2,2,2

Because you're looking for a square root and you can "loop" two 2s together, you can take one set out:

would be your final answer.

Hope I helped :)