So the closest integer above the square root of 3 is 2, and the closest integer below the square root of 89 is 9. (square root of 4 and 81, respectively.)
So we just want to add together all numbers between (including) 2 and 9.
So,
2 + 3 + 4 + 5 + 6 + 7 + 8 + 9
Or,
11 * 4
44
