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There are infinitely many rational numbers between them.Consider for example, 31/10, 32/10, ... , 49/10. The square root of each is irrational.

Or consider 3001/1000, 3002/1000, ..., 4999/1000. Again, each square root is irrational.


Note, though, that I did not list hundredths. That is because sqrt(36/100) = 6/10 is rational.

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