8 and 9
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The square root of 92 will be +/- 9.59. It lies between the consecutive integers of 9 and 10.
96 cannot lie between two consecutive whole numbers.
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).
It's the other way around. The square root of 22 lies between 4 and 5
3 and 4