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Oh, what a happy little question! Square numbers are numbers that result from multiplying a number by itself. Between 40 and 100, the square numbers are 49 (7 x 7), 64 (8 x 8), and 81 (9 x 9). Isn't it wonderful to see these beautiful numbers all lined up like a row of friendly little trees?
The sum of the integers between 101 and 300 inclusive is equal to ((101+300) x 200) / 2 = 40100.
There are 10 square numbers
4,9,16,25,36,49,64,81
The square root of 75 lies between 8 and 9.
The square root of 60 is a single number; you can't have other numbers "between" it. It does work the other way, though - the square root of 60 is between other numbers.