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Q: The positive square root 92 is between what pair of integers?

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-3 and 6 is one possible pair.

-10 and -9 is one possible pair.

THere are two pair of consecutive integers. 52 = 25 < 30 < 36 = 62 So, one pair is 5 and 6 and the other pair is -6 and -5.

There are 1,963 such integers. Every factor of a number has a pair. The only time there will be an odd number of factors is if one factor is repeated, ie the number is a perfect square. So the question is really asking: how many positive integers less than 2008 (in the range 1 to 2007) are not perfect squares. √2007 = 44 and a bit (it lies between 44 and 45) So there are 44 integers less than (or equal to) 2007 which are perfect squares → 2007 - 44 = 1963 integers are not perfect squares in the range 1-2007 and have an even number of factors (divisors).

The lowest common factor of any pair of positive integers is 1.

sqrt(89) = -9.4 or +9.4 So one possible pair of consecutive integers between the square roots of 89 are 2 and 3.

For each pair of such integers, find the difference between the absolute values of the two integers and allocate the sign of the bigger number to it.

Take any negative integers, say -5 and -10, their sum is -15 which is smaller than both of them. We could have used 0 as well, so I should have said any non-positive integers. To see that is does not work with positive integers, take 5 and 10 whose sum is 15 which is BIGGER than either one.

There are infinitely many numbers, but a simple pair to remember is 1 and 139. Since 139 is a prime, this is the only solution with a pair of positive integers.

It can be proven that it is impossible to find a pair of integers, p and q, such that p/q = sqrt(14).

The square root is between 5 and 6.

Every positive rational number and its negative are the two square roots of the same positive rational number.

{0, 1, 2, 3, 4, 5} and {2, 3, 4, 5, 6, 7}

The square root of 73 is between 8 and 9.

The answer is 2 and 3

There are infinitely many pairs of numbers including many pairs of positive integers. An easy pair to remember is 1 and 675.

You cannot. The sum of negative integers will be negative.

There is no unique pair of numbers that satisfies these requirements. Suppose a and b is such a pair, and sqrt(105) = x then you want a < x < b But a < (a+x)/2 < x < (b+x)/2 < b So that (a+x)/2 and (b+x)/2 are a closer pair. and you can then find a closer pair still - ad infinitum. The question can be answered (sort of) if it asked about "integers" rather than "numbers". 100 < 105 < 121 Taking square roots, this equation implies that 10 < sqrt(105) < 11 so the answer could be 10 and 11. But (and this is the reason for the "sort of") the above equation also implies that -11 < sqrt(105) < -10 giving -11 and -10 as a pair of consecutive integers. So, an unambiguous answer is possible only if the question specifies positive integers.

35.9999999999 and 36.0000000001

There are infinitely many answers: 1+a/b and 2-a/b for any pair of positive integers a and b, with a<b.

Yes. There is an injective function from rational numbers to positive rational numbers*. Every positive rational number can be written in lowest terms as a/b, so there is an injective function from positive rationals to pairs of positive integers. The function f(a,b) = a^2 + 2ab + b^2 + a + 3b maps maps every pair of positive integers (a,b) to a unique integer. So there is an injective function from rationals to integers. Since every integer is rational, the identity function is an injective function from integers to rationals. Then By the Cantor-Schroder-Bernstein theorem, there is a bijective function from rationals to integers, so the rationals are countably infinite. *This is left as an exercise for the reader.

The pair of consecutive integers which add up to 55 are 27 and 28. Therefore, any consecutive pair of numbers below 27 and 28 add up to a total less than 55.

They are; 8 and 9 but the square root of 68 is about 8.246211251

Select any 4 integers between 0 and 10. These will represent the first of the ordered pairs. For each of these select any one of the integers between -12 and 5. These need not be different from each other and will represent the second of the ordered pair. These four pairs defines a function.There are more than 32 nonillion (32,000,000,000,000,000,000,000,000,000) possible functions, so I hope you will understand why I do not wish to list them.

The least common factor is 1. (The least common factor of any two or more positive integers is always 1.)