Final answer:
Between the squares of 500 and 501, there are 999 non-square numbers. This is derived from the difference between 500² and 501² minus one square number that falls within that range.
Step-by-step explanation:
The question asks us to find the number of non-square numbers between 500² and 501². A non-square number is any integer that is not the square of an integer. First, we must calculate the squares of the two given numbers. Since 500² equals 250,000 and 501² equals 251,001, the range between them is from 250,001 to 251,000. The number of integers in this range is 251,000 - 250,000, which is 1,000. However, since we are only interested in non-square numbers, we should subtract the number of square numbers in this range.
To find the squares in this range, note that the only squares are the squares of the numbers 501 since 500² is our starting point. Therefore, we have 1 square number (501²) in this range.
Finally, we subtract the number of square numbers from the total number to find the number of non-square numbers: 1000 - 1 = 999. Thus, there are 999 non-square numbers between 500² and 501².