A square root of a number is a number such that . Generally, the square root only takes the positive value of . This can be altered by placing a before the root. Thus is a square root of if is the square of .
The square root (or the principle square root) of a number is denoted . For instance, . When we consider only positive reals, the square root function is the inverse of the squaring function.
Square roots can also be written in exponential notation, so that is equal to the square root of . Note that this agrees with all the laws of exponentiation, properly interpreted. For example, , which is exactly what we would have expected. This notion can also be extended to more general rational, real or complex powers, but some caution is warranted because these do not give functions. In particular, if we require that always gives the positive square root of a positive real number, then the equation does not hold. For example, replacing with gives on the left but gives on the right.