Square them both.  Choose a number between their
squares which is not the square of a rational 
number, then take the square root of that number.

In the case of 4 and 6,

42=16 and 62=36,

Choose any number between 16 and 36 which is not
the square of a rational number.  [Any integer
between them other than 25 will do].

Say we pick 26, then

 is irrational and between 4 and 6.
since it is approximately 5.099019514

[Some people might think you can just multiply the two
numbers together and take the square root, but sometimes 
this will give a rational number, for instance, with 8&2.]

Edwin