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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.
In the same way we saw that only the square roots of square numbers are rational, we could prove that only the nth roots of nth powers are rational. Thus, the 5th root of 32 is rational, because 32 is a 5th power, namely the 5th power of 2. But the 5th root of 33 is irrational. 33 is not a perfect 5th power.