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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.

Q: Between which two rational numbers does the square root of 85 lie?

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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.

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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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No. Lots of square roots are not rational. Only the square roots of perfect square numbers are rational. So for example, the square root of 2 is not rational and the square root of 4 is rational.

Write both numbers as decimal numbers, then look for terminating decimals between the two.

Infinitely many. In fact, there are more irrational numbers between them than there are rational numbers.Infinitely many. In fact, there are more irrational numbers between them than there are rational numbers.Infinitely many. In fact, there are more irrational numbers between them than there are rational numbers.Infinitely many. In fact, there are more irrational numbers between them than there are rational numbers.

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.

Some square roots are rational but the majority are not.

Yes. The square root of 81 is 9 - a natural number and all natural numbers are rational numbers.

They are NOT rational numbers, so the question is misguided.

No, and I can prove it: -- The product of two rational numbers is always a rational number. -- If the two numbers happen to be the same number, then it's the square root of their product. -- Remember ... the product of two rational numbers is always a rational number. -- So the square of a rational number is always a rational number. -- So the square root of an irrational number can't be a rational number (because its square would be rational etc.).

The square root of 61.93 is irrational. Since rational numbers are infinitely dense there cannot be a closest rational.