Proof Writing & Problem Solving · Easy problem

A proof by contradiction shows that a rational number plus an irrational number is always irrational, and another shows $\sqrt{6}$ is irrational. Using these facts, how many of the following six numbers are rational?

$3 + \sqrt2, \quad (2 + \sqrt2) - \sqrt2, \quad 5 - \sqrt2, \quad (1 + \sqrt2) + (1 - \sqrt2), \quad \dfrac{\sqrt8}{\sqrt2}, \quad \sqrt2 \cdot \sqrt3$