Page "Compass and straightedge constructions" Paragraph 32

Since the field of constructible points is closed under square roots, it contains all points that can be obtained by a finite sequence of quadratic extensions of the field of complex numbers with rational coefficients.

By the above paragraph, one can show that any constructible point can be obtained by such a sequence of extensions.

As a corollary of this, one finds that the degree of the minimal polynomial for a constructible point ( and therefore of any constructible length ) is a power of 2.

In particular, any constructible point ( or length ) is an algebraic number, though not every algebraic number is constructible ( i. e. the relationship between constructible lengths and algebraic numbers is not bijective ); for example, is algebraic but not constructible.