# Show that 2^(1/3) + 3^(1/3) is irrational.

 P: 114 The hint suggests to find a polynomial with integer coefficients. You have the right idea cubing, but there's a little more. You found $$x_0^3=5+\sqrt[3]{6}(\sqrt[3]{2}+\sqrt[3]{3})$$. But you can simplify that even more, by substituting $$x_0$$ in for $$\sqrt[3]{2}+\sqrt[3]{3}$$, to get $$x_0^3=5+\sqrt[3]{6}x_0$$ Then try to get rid of the final cube root, and you have an integer polynomial.