here, there is not much to do after the hint the book gave.
For every positive irrational number b, there exists an irrational number a with 0<a<b
Let b be any positive irrational number. Consider a = b/2. Note that a<b, and since a is obtained by dividing an irrational number by a rational number, a is irrational. And since a is half of a positive number, we have a>0. Thus we have 0<a<b, where a and b are irrational, as desired