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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 0 is by definition either 0 or a zero divisor, and where zero divisors do not exist (such as in quaternions and, generally, in division algebras), it is uniquely 0. It is not necessarily true in general rings, where Z/n2Z for any natural n provides an easy counterexample.