Very rarely.
Square roots are only whole numbers for perfect squares.
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The square root of 31 falls between the whole numbers 5 and 6.
No. Square roots of whole numbers that don't result in whole numbers (e.g. the square root of 64 is 8), are considered to be "Irrational Numbers".
The square root of 110 is an irrational number and so it cannot be any two whole numbers.
The square root of 135 is 11.61895. The two whole numbers closest would be 11 and 12.
The nearest whole number to the square root of 274 is seventeen (17).