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Question:

Find three different irrational numbers between the rational numbers 5/7 and 9/11.

Solution:

57=0.714285714285...=0.¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯714285and911=0.8181...=0.¯¯¯¯¯¯81.Here, the two decimal expansions are non-terminating recurring.Hence,57and911are 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 three different irrational number between57and911can be:0.750750075000075...0.767076700767...0.808008000800008...NOTE:This is three of the various possible answers. It might have different solution.