The answer is sqrt(7) since there are infinitely many numbers between sqrt(7) and any other number. So if x is a number laying claim to being the closest, then there are infinitely many numbers between x and sqrt(7) and so each one of them is closer to sqrt(7) totally invalidating x's claim of being closest.
The closest integers, are -3 and +3.
The square root of 135 is 11.61895. The two whole numbers closest would be 11 and 12.
The square root of 162 is approximately 12.727. Therefore, the two whole numbers closest to the square root of 162 are 12 and 13.
The square root of 8 is approximately 2.83. The two whole numbers closest to this value are 2 and 3.
13 and 14. The square root of 192 is 13.8564065, so the two whole numbers that are closest are 13 and 14.
6 and 7. The square root of 37 is 6.0827625, so the two whole numbers that are closest are 6 and 7.
The square root of 28 is approximately 5.29. The two whole numbers closest to this value are 5 and 6.
The numbers are -14 which is closest to -sqrt(192) and 14 which is closest to sqrt(192).
-10 and +10.
They are 12 and 13
The two whole number which are -6 (nearest to the negative square root of 34) and +6 (nearest to the positive square root of 34).
-7 and +7 are the two numbers.
4x4=16, and 5x5=25, so 4 and 5 are the whole numbers closest to the square root of 19. [And incidentally of all the square roots of all the whole numbers between 16 and 25.]