Algebraic Number/Examples/Root of (2 plus Root 3)

Example of Algebraic Number

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

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

We have that:

Thus $\sqrt {2 + \sqrt 3}$ is a root of $x^4 - 4 x^2 + 1 = 0$.

Hence the result by definition of algebraic number.