How do you simplify: the square root of -500?

The square root of a negative number is called an imaginary number.

For instance, ##5i^2## would be -25. To find the square root of -500, we have to pretend that it is a positive 500, and simply add an ##i## to the end of our answer. The square root of 500 would be 22.360679775, so the square root of -500 is ##22.360679775i##.