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 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
-7 and +7 are the two numbers.
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).
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.]
14 and 15, closer to 14.