What's the sum of all the integers between √3 and √89 ?

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