96 cannot lie between two consecutive whole numbers.
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136 cannot lie between two consecutive whole numbers.
8 and 9
The square root of 92 will be +/- 9.59. It lies between the consecutive integers of 9 and 10.
3 and 4
I suspect you are really asking for between which two whole numbers does the square root of 150 lie. The square root of 150 lies between 12 and 13 (mathematically: 12 < √150 < 13).