Finding the Smallest Whole Number for a Perfect Square
To find the smallest whole number that, when added and subtracted by 2120, will make it a perfect square, we need to follow a systematic approach. Let's break it down step by step.

Step 1: Express the Problem Mathematically
Let's denote the smallest whole number we are looking for as x. So, we have:
(x + 2120) + (x - 2120) = n^2
Simplify the equation:
2x = n^2
x = (n^2)/2

Step 2: Determine the Constraints
To find the smallest whole number, the value of n should be a positive integer. Hence, n must be an odd number since (n^2)/2 is an integer.

Step 3: Find the Smallest Whole Number
Now, we need to find the smallest odd number n that when squared gives us a whole number. Let's start from the smallest odd number, which is 1.
n = 1
x = (1^2)/2 = 1/2 (not a whole number)
n = 3
x = (3^2)/2 = 9/2 (not a whole number)
n = 5
x = (5^2)/2 = 25/2 = 12.5 (not a whole number)
n = 7
x = (7^2)/2 = 49/2 = 24.5 (not a whole number)
n = 9
x = (9^2)/2 = 81/2 = 40.5 (not a whole number)
n = 11
x = (11^2)/2 = 121/2 = 60.5 (not a whole number)
n = 13
x = (13^2)/2 = 169/2 = 84.5 (not a whole number)

Step 4: Conclusion
After trying out a few odd numbers, we see that none of them gives us a whole number when plugged into the equation. Therefore, there is no smallest whole number that satisfies the given condition.