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Q: Which pair of numbers does the square root of 103 fall between?

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

-5 and -4 or 4 and 5

Ordered pair (s)

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

Call the integer square roots of the specified pair of numbers l and g for lesser and greater respectively. Then, from the problem statement, g2 - l2 = 105. Possible values for l2 are successively 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, .... , and corresponding values for g2 are 106, 109, 114, 121, ... etc. The first of the latter series that is a perfect square number is 121. Therefore, the square numbers are 121 and 16.

Related questions

35.9999999999 and 36.0000000001

5 and 6

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

4 and 5 because the square root of 18 is about 4.242640687

17 and 19

53 and 55.

9 and 10 9 x9 =81 10 x 10 = 100

26 falls between 25 and 27.

58 falls between 57 and 59.

18 falls between 17 and 19.

The square root is between 5 and 6.

The square root of 73 is between 8 and 9.

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