# Algebraic Number/Examples/Root 2

## Example of Algebraic Number

$\sqrt 2$ is an algebraic number.

## Proof

We have that:

 $\ds x^2 - 2$ $=$ $\ds 0$ $\ds \leadsto \ \$ $\ds x$ $=$ $\ds \pm \sqrt 2$ Quadratic Formula

Thus $\sqrt 2$ is a root of $x^2 - 2$.

Hence the result by definition of algebraic number.

$\blacksquare$