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 
.
See also
Cube Root, i, nth Root, Principal Root of Unity, Radical, Square Root, Surd
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Cite this as:
Weisstein, Eric W. "Principal Square Root." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/PrincipalSquareRoot.html