0.7172737475767778....

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0.7172737475767778....

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therefore, the irrational number between 5/7 and 7/9 is √5/7×7/9=√5/9=√5/3.

There are many irrational numbers between two rational numbers.

7/9=0.7 recurring

Now, we have to find irrational numbers between 0.714285 recurring and 0.7 recurring.

There are infinitely many such numbers.

Two of them could be:

0.710710071000.....

0.713713371333....

Note*- I have used "recurring" because its symbol is not available.