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Question

Insert any two irrational numbers between 47 and 57.

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Solution

57=0.714285714285...=0.¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯714285
and 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.

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