The two perfect squares nearest to 114 are 100 (102) and 121 (112).
Consequenly, the two whole numbers (integers) closest to √114 are 10 and 11.
Note that √114 ≈ 10.677 (3dp)
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The whole number closest to the square root of 65 is 8. The whole number closest to the square root of 65 is 8.
For smaller numbers, this is best done by trial and error.
39
12 (122 = 144, the closest square root)
3