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.

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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

can then be distinguished. Since either choice is possible, there is no ambiguity in defining
as "the" square root of

SEE ALSO: Cube Root, i, nth Root, Principal Root of Unity, Radical, Square Root, Surd

Weisstein, Eric W. "Principal Square Root."From Web Resource. Web Resources

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