How many perfect squares are there between 5 and 50? This question may seem simple at first glance, but it requires a bit of mathematical thinking to find the answer. In this article, we will explore the number of perfect squares within the given range and discuss the process of identifying them.
The first step in solving this problem is to determine the smallest and largest perfect squares within the range of 5 to 50. A perfect square is a number that can be expressed as the product of an integer with itself. For example, 4, 9, 16, 25, 36, and 49 are all perfect squares.
To find the smallest perfect square greater than 5, we can start with the square of the integer 3, which is 9. This is the first perfect square that exceeds 5. Next, we need to find the largest perfect square less than 50. The square of the integer 7 is 49, which is the largest perfect square within the range.
Now that we have identified the smallest and largest perfect squares within the range of 5 to 50, we can count the number of perfect squares between them. By listing the perfect squares between 9 and 49, we can see that there are a total of six perfect squares: 9, 16, 25, 36, 49, and 64. However, since 64 is not within the range of 5 to 50, we exclude it from our count.
Therefore, the answer to the question “How many perfect squares are there between 5 and 50?” is six. This demonstrates the importance of understanding the properties of perfect squares and how to identify them within a given range. By applying mathematical reasoning and a bit of patience, we can solve this problem and gain a deeper understanding of number theory.
