In this particular case it is enough to find a polynomial (with integer coefficients) that has this as a root. It will be a polynomial of degree 8.Hi,
i cant figure out this problem in my algebra book
I thought it was interesting that this thing was rational though...
anyone know how to start it?
The easiest way I can think is in terms of vector spaces over Q. (Meaning that you can only use rational numbers as scalars, rather than arbitrary real or complex numbers)Also, intuitively, it seems true that the sum of algebraic numbers is also algebraic. On the other hand, there is probably an easier way.