What Is the Square Root of Negative 4?

Technically, the square root of a negative number cannot be taken, but if imaginary numbers are allowed, the answer would be 2i. It can be tempting for those people just learning how to deal with square roots to assume the square root of -4 would be -2, but this does not work because when -2 is multiplied by -2, the result is 4 rather than -4.

Mathematicians use the imaginary number "i" in these kinds of expressions to make simplifying negative radicals and performing other operations on them easier as well. The imaginary unit "i" represents the square root of -1.