How many five-digit integers are perfect squares?

The smallest 5-digit number is 10000 and its square-root is 100.

The largest 5-digit number is 99999 and its square-root is 316.23.

Thus the square of all integers between 100 and 316 inclusively will yield a perfect square between 10000 and 99999.

How many integers are there?

To determine the number of five-digit integers that are perfect squares, we need to find the range of five-digit numbers and then determine how many of them are perfect squares.

The range of five-digit numbers can be determined by finding the smallest and largest five-digit numbers. The smallest five-digit number is 10,000, and the largest five-digit number is 99,999. Therefore, we need to determine how many of these numbers are perfect squares.

To find the number of perfect squares within this range, we need to consider the square root of the smallest and largest five-digit numbers. The square root of the smallest five-digit number, 10,000, is 100, and the square root of the largest five-digit number, 99,999, is approximately 316. Thus, we need to determine how many perfect squares are between 100 and 316.

To do this, we subtract the integer square root of the smallest number from the integer square root of the largest number and add 1, as both ends are inclusive. In this case, it will be: (sqrt(99999) - sqrt(10000)) + 1.

Using a calculator, we find that sqrt(99999) is approximately 316.22, and sqrt(10000) is 100. Therefore, the number of perfect squares between 100 and 316 is (316 - 100) + 1 = 217.

Thus, there are 217 five-digit integers that are perfect squares.