## Quick Reference

For any real number *a*, an *n*-th root of *a* is a number *x* such that *x*^{n}=*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 *x*^{n}=*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 *x*^{n}=*a*, and it is denoted by For example, ∛−8 = −2.

*Subjects:*
Mathematics.

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