“nth root”的概念、定义、习题解题方法及翻译-数学辞典

单词

nth root

释义

nth root

For any real number a, an nth 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<0, there is no real number x such that xⁿ = a. If a > 0, there are two such numbers, one positive and one negative. For a≥0, the notation $inline$ is used to denote quite specifically the non-negative nth root of a. For example, $inline$ , and 16 has two real 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 an $inline$ . For example, $inline$ .

For a non-zero complex number a, there are n complex numbers z such that zn = a, which may also be referred to as nth roots of a. In the Argand diagram these nth roots form the vertices of a regular n-gon.

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