No.
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No. In general, the square root of a positive integer is either a whole number, or an irrational number.
9 and 10
No, a square root doesn't have to be a whole number. The square root of 2.25 is 1.5. It could be said that most square roots are not whole numbers. Take just the first few integers (counting numbers). Find the square roots of the numbers 1 through 10 and you'll find three of the numbers have whole number square roots (1, 4 and 9). The other seven don't. For the numbers 11 through 20, there is only 1 number with a whole number square root (16).
92 = 81 and 102 = 100 so the square root of any number between 81 and 100 would lie between 9 and 10.
No 81 is (9 x 9) 100 is (10 x 10) 88 is not - at least not of a whole number Square root is 9.3808315 etc