For how many different integers is the square of the integer less than 144?
First find the square roots of 144, which are 12 and -12.
So now you know that the square of any integer less than 12 and greater than -12 would be less than 144.
That includes:
0, ±1, ±2, ±3, ±4, ±5, ±6, ±7, ±8, ±9, ±10, ±11
Which would be 23 integers, including zero.