A constant is a value that does not change, an integer is a positive whole number.
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A rational number which is an integer can be simplified to a form in which the denominator is 1. That is not possible for a rational number which is not an integer.
√479 ≈ 21.89 √500 ≈ 22.36 Making 22 as the integer between them.
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None. 1000 does not have an integer square root. 312 = 961 and 322 = 1024 and there is no integer between 31 and 32 so there can be no integer whose square is 1000.
The difference between any numbers is always positive.