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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 square root of a non-negative number is used in the definition of Euclidean norm (and distance), as well as in generalizations such as Hilbert spaces. It defines an important concept of standard deviation used in probability theory and statistics.