A real number xR is called algebraic if there exists integers a0x^n+an1x^n1+.....+alx+a0=0.

Show that (2)^1/2,(2)^1/3, and 3+(2)^1/2 are algebraic.

Fix n in N and let An be the algebraic numbers obtained as roots of polynomials with integer coefficients that have degree n. Using the fact that every polynomial has a finite number of roots, show that is countable.

The algebraic definition is getting me confused.