Algebraic Number/Examples/Cube Root of (2 plus Root 2)

Example of Algebraic Number

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

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

We have that:

Thus $\sqrt [3] {2 + \sqrt 2}$ is a root of $x^6 - 4 x^3 + 2 = 0$.

Hence the result by definition of algebraic number.