1. The problem statement, all variables and given/known data Given any 2 reals a<b there exists an irrational number t such that a<t<b . It tells us to use a theorem that states there is a rational number between any 2 reals. 3. The attempt at a solution so If we use this and pick reals of the form p=a-√2 and q=b-√2 so now we have a-√2<t<b-√2 , and t is a rational number. then we add √2 to everything so we get a<t+√2<b so now t+√2 is irrational , so now we have an irrational between any 2 reals.