Prove that 5 - 3√2 is irrational. You may use the fact that √2 is irrational.

Step 1. Suppose the opposite. Suppose $5 - 3\sqrt{2} = s$, where $s$ is rational.

Step 2. Get the root alone. $3\sqrt{2} = 5 - s$, so $\sqrt{2} = \dfrac{5 - s}{3}$.

Step 3. The contradiction. $5 - s$ is rational, and so is a third of it. Then $\sqrt{2}$ would be rational, but it is irrational.