Algebraic Number/Examples/Cube Root of 2 plus Root 3

Example of Algebraic Number

 * $\sqrt [3] 2 + \sqrt 3$ is an algebraic number.

Proof
Let $x = \sqrt [3] 2 + \sqrt 3$.

We have that:

Thus $\sqrt [3] 2 + \sqrt 3$ is a root of a non-zero polynomial with rational coefficients, namely $x^6 - 9 x^4 - 4 x^3 + 27 x^2 - 36 x - 23 = 0$.

By the definition of an algebraic number, we get the desired result.