Let "a" and "b" be two rational numbers, with b > a.

Let c = b - a is their difference.

Consider the irrational number  and take small part of it, , with an integer "n", so small, that  is less than (b-a).

Now consider the number .

It is 

1. between "a" and "b", and 

2. it is irrational.


It gives the answer to your question.


Thank you for asking.