Insert any two irrational numbers between 47 and 57.
57=0.714285714285...=0.¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯714285and 47=0.571428571428...=0.¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯571428.
Here, the two decimal expansions are non-terminating recurring.
Hence, 57 and 47 are two rational numbers.
We know, between any two rational numbers, there are infinitely many irrational numbers.
An irrational number has non-terminating non-recurring decimal expansions.
Then two different irrational number between 57 and 47 can be:
0.5918264201001... and 0.601001000100001...
NOTE:
This is two of the various possible answers. It might have different solution.