The integers that are closest to the number in the middle would be 11 and 12.
Perfect squares are those integers whose square root is an integer.
Let x-a be the closest perfect square less than x,
and let x+b be the closest perfect square more than x, then we get x-a < x < x+b (no perfect square in between x-a and x+b, except possibly x itself).
Then, we get:
[tex]\sqrt{x-a} < \sqrt{x} < \sqrt{x+b}[/tex]
Thus, [tex]\sqrt{x-a} and \sqrt{x+b}[/tex]are the closest integers, less than and more than the value of[tex]\sqrt{x}[/tex]. (assuming x is a non-negative value).
The given number is -122.
[tex]121 < 122 < 144\\\\\\sqrt{121} < 122 < \sqrt{144} \\\\11 < 122 < 12[/tex]
It would be 11 and 12.
Learn more about square root here:
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