Principal Square Root

The unique nonnegative square root of a nonnegative real number. For example, the principal square root of 9 is 3, although both  and 3 are square roots of 9.

The concept of principal square root cannot be extended to real negative numbers since the two square roots of a negative number cannot be distinguished until one of the two is defined as the imaginary unit, at which point  and  can then be distinguished. Since either choice is possible, there is no ambiguity in defining  as "the" square root of .