Radical - Radical (English spelling)

Japanese: べき根(冪根) - べきこん（英語表記）radical

For a number a and a natural number n , the number that becomes a when raised to the nth power is called the nth root of a . In particular, when n = 2 or 3, they are also called the square root and cube root, respectively. The square root, cube root, ..., nth root of a are called the power root or radical root of a. When a is a positive number, a has exactly one positive nth root. This is expressed by ⁿ (when n = 2). The symbols ⁿ √ and √ are called root symbols. If a is a real number and n is odd, a has exactly one nth root in the range of real numbers. This is also expressed by ⁿ . In general, when α is a complex number, when considering the range of complex numbers, there are n nth roots of α (however, when α = 0, there is only one).

Source: Heibonsha World Encyclopedia, 2nd Edition Information

Japanese:

ある数aと自然数nについて，n乗してaとなる数をaのn乗根という。とくにn＝2,3のとき，それぞれ平方根，立方根とも呼ぶ。aの2乗根，3乗根，……，n乗根をaのべき根または累乗根という。aが正の数のとき，aはただ一つ正のn乗根をもつ。これをⁿ　(n＝2のときは)で表す。記号ⁿ√，√を根号と呼ぶ。aが実数でnが奇数なら，aは実数の範囲にただ一つn乗根をもつ。これもⁿ　で表す。　一般にαが複素数のとき，複素数の範囲で考えると，αのn乗根はn個ある(ただし，α＝0のときは1個)。

出典　株式会社平凡社世界大百科事典第２版について　情報

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