What is a rational and irrational number between 9.5 and 9.8

Some rational numbers in that range:

9.6,  9.61,  9.62,  9.7,  9.70004,  9.70009,  9.7009,  9.709, 9.719, 

9.729,  9.739,  9.759,  9.779,  9.789,  9.799,  9.7991,  9.7992, etc.

The one exactly midway between  9.5  and  9.8  is called
their "average".  You find it like this:

             (1/2) (9.5 + 9.8) = (1/2) (19.3) =  9.65 .

Irrational numbers are harder to find.
You can't just write them down, because any number that
you can completely write down on paper with digits is a
rational number.

     √91,  √92,  √93,  √94,  √95,  and  √96

are all in that range, and I think they're all irrational.

The correct answer is -20y