Constructible numbers

Abstract

A number which can be represented by a finite number of additions, subtractions, multiplications, divisions, and finite square root extractions of integers. Such numbers correspond to line segments which can be constructed using only straightedge and compass. All rational numbers are constructible, and all constructible numbers are algebraic numbers (Courant and Robbins 1996, p. 133). If a cubic equation with rational coefficients has no rational root, then none of its roots is constructible...