Let a = 0.5 = 0.50

And, b = 0.55

We observe that in the second decimal place a has digit 0 and b has digit 5, therefore a < b

so, if we consider irrational numbers

x = 0.51051005100051...

y = 0.530535305353530...

We find that a < x < y < b

Hence, x and y are required irrational numbers.