Question

find any two irrational numbers between 0.5 and 0.55

Answer 1

The two irrational numbers between 0.5 and 0.55 are of non-terminating and non-repeating decimal numbers. For example, 0.512122122212222 ..... and 0.539399399939999....

Answer 2

Irrational numbers are those no.s which cannot be expressed as a ratio of 2 integers. 
Irrational no.s are non terminating and non repeating.
So two irrational no.s between 0.5 and 0.55 are
0.505500555000............             and
0.525522555222............
Like this infinite patterns can be formed