How many positive integers less than 500 are perfect squares? This question may seem simple at first glance, but it requires a deeper understanding of mathematics to find the answer. In this article, we will explore the concept of perfect squares and calculate the number of such integers that are less than 500.
Perfect squares are numbers that can be expressed as the product of an integer with itself. For example, 1, 4, 9, 16, and 25 are all perfect squares because they can be written as 1 x 1, 2 x 2, 3 x 3, 4 x 4, and 5 x 5, respectively. To find the number of perfect squares less than 500, we need to identify the largest integer whose square is still less than 500.
We can start by finding the square root of 500, which is approximately 22.36. Since we are looking for integers, we can round down to 22. Now, we need to determine the number of perfect squares between 1 and 22. This can be done by counting the squares of each integer from 1 to 22.
By calculating the squares of these integers, we get the following perfect squares: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400, 441, and 484. Counting these numbers, we find that there are 22 perfect squares less than 500.
In conclusion, there are 22 positive integers less than 500 that are perfect squares. This result highlights the importance of understanding the properties of perfect squares in mathematics and provides a simple yet effective method for finding the number of such integers within a given range.
