To prove that √2 is an irrational number, a teacher begins by assuming that it is a rational number and then proceeds to show how this assumption is not feasible. This is an example of proof by

Proof by contradiction (reductio ad absurdum) involves assuming the opposite of what is to be proved and showing that this assumption leads to a contradiction or impossibility. The classic proof that √2 is irrational uses this method - assuming √2 is rational and deriving a contradiction.