Algebraic Number/Examples/Root 3 plus Root 2

Example of Algebraic Number

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

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

We have that:

Thus $\sqrt 3 + \sqrt 2$ is a root of $x^4 - 10 x^2 + 1 = 0$.

Hence the result by definition of algebraic number.