Final answer:
There are 31 perfect squares between 550 and 3025, which are the squares of the whole numbers 24 through 54.
Step-by-step explanation:
To find how many perfect squares are between 550 and 3025, we locate the smallest and largest whole numbers whose squares are within this range. The square root of 550 is approximately 23.45, so the smallest whole number we can square to get a result greater than 550 is 24. The square root of 3025 is exactly 55, so the largest number we can square to get a result less than 3025 is 54. Therefore, we want to find all the perfect squares that come from squaring the integers from 24 through 54.
We can calculate this by subtracting 23 from 54 (because 23 is the last integer whose square is below our range), which gives us 31 perfect squares in this range. To visualize this, the numbers 242, 252, ..., 542 are all perfect squares greater than 550 and less than 3025.