It is not possible to answer this question sensibly, since rational numbers form a continuum. So for any pair of rational numbers surrounding sqrt(85), it is possible to give another pair of rationals that surrounds it but such that the rationals are closer together. And this sequence is infinite.
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There are no rational numbers between sqrt(-26) and sqrt(-15). The interval comprises purely imaginary numbers.
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Write both numbers as decimal numbers, then look for terminating decimals between the two.
There are an infinite number of rational numbers between these two numbers, but the only positive integer between these numbers is 6.
Only if the square root of the numerator and the square root of the denominator are both rational numbers.