How many perfect squares are between 1 and 50? This is a question that might seem simple at first glance, but it requires a bit of mathematical thinking to find the answer. In this article, we will explore the concept of perfect squares and determine the exact number of them within the given range.
Perfect squares are numbers that can be expressed as the square of an integer. For example, 1, 4, 9, 16, 25, 36, 49, and so on, are all perfect squares. These numbers are formed by multiplying an integer by itself. To find the perfect squares between 1 and 50, we need to identify the integers whose squares fall within this range.
The smallest perfect square greater than 1 is 4, which is the square of 2. As we continue to square integers, we find that the next perfect squares are 9 (3 squared), 16 (4 squared), 25 (5 squared), 36 (6 squared), and 49 (7 squared). At this point, we have identified all the perfect squares between 1 and 50.
To confirm that there are no more perfect squares within the given range, we can consider the square root of 50. The square root of 50 is approximately 7.07, which means that any integer greater than 7 will have a square greater than 50. Since 7 squared is 49, which is the largest perfect square less than or equal to 50, we can conclude that there are no more perfect squares between 1 and 50.
In total, we have identified five perfect squares between 1 and 50: 4, 9, 16, 25, and 49. This exercise demonstrates the simplicity and beauty of mathematics, as we can use basic principles to find solutions to seemingly complex questions. So, the answer to the question “How many perfect squares are between 1 and 50?” is five.
