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n-th root


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For any real number a, an n-th root of a is a number x such that xn=a. (When n=2, it is called a square root, and when n=3 a cube root.)

First consider n even. If a is negative, there is no real number x such that xn=a. If a is positive, there are two such numbers, one positive and one negative. For a≥0, the notation is used to denote quite specifically the non-negative n-th root of a. For example, ∜16 = 2, and 16 has two fourth roots, namely 2 and −2.

Next consider n odd. For all values of a, there is a unique number x such that xn=a, and it is denoted by For example, ∛−8 = −2.

Subjects: Mathematics.


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