Rational numbers are numbers that can be expressed as fractions and hence can be expressed as where and are integers and not equal to 0. All rational numbers can be expressed as lowest terms. These are some of the important things to consider in proving that square root of 2 is irrational.
In proving the theorem, you also should be familiar with proof by contradiction. This proof method requires the negative assumption of statement that you are trying to prove, and then, finding a contradiction along the proof. When this happens, then your assumption must be false and hence the statement that you are trying to proof is true. You will need to study this concept for you to understand the proof.