Let F be a field and α be algebraic (http://planetmath.org/Algebraic) over F. Then α is a radicalPlanetmathPlanetmath over F if there exists a positive integer n with αnF.

Note that, if K/F is a field extension and α is a radical over F, then α is automatically a radical over K.

Following are some examples of radicals:

  1. 1.

    All numbers of the form abn, where n is a positive integer and a and b are integers with b0 are radicals over .

  2. 2.

    The number 24 is a radical over (2) since (24)2=2(2).

Title radical
Canonical name Radical1
Date of creation 2013-03-22 16:55:36
Last modified on 2013-03-22 16:55:36
Owner Wkbj79 (1863)
Last modified by Wkbj79 (1863)
Numerical id 9
Author Wkbj79 (1863)
Entry type Definition
Classification msc 12F05
Classification msc 12F10
Related topic RadicalExtension
Related topic NthRoot
Related topic SolvableByRadicals
Related topic Radical6