Let us take an example.

Example: Prove that √5 is irrational.

Answer:

Let us suppose that √5 is a rational number. So, it can be represented as p/q form

=> √5 = p/q

Take square on both side, we get

=> 5 = p²/q²

=> 5q² = p² ..............1

So p² is divisible by 5.

=> p is divisible by 5.

Let p = 5x          (x is a positive integer)

Now p² = 25c²

From equation 1, we get

      5q² = 25c²

=> q² = 5c²

So, q is divisible by 5

Thus p and q has a common factor 5. It is contradiction of our assumption.

So, √5 is an irrational number.