Number of Type Rational r plus s Root 2 is Irrational

Theorem
Let $r, s \in \Q$ be rational numbers.

Then $r + s \sqrt 2$ is irrational.

Proof
$t = r + s \sqrt 2$ be rational.

Then:
 * $\sqrt 2 = \dfrac {t - r} s$ is also rational.

This contradicts the fact that Square Root of 2 is Irrational.

Hence the result by Proof by Contradiction.