What is the perfect square of 252? 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 how to determine the perfect square of 252.
A perfect square is a number that can be expressed as the square of an integer. For example, 1, 4, 9, 16, and 25 are all perfect squares because they can be written as the squares of 1, 2, 3, 4, and 5, respectively. To find the perfect square of 252, we need to identify an integer whose square is equal to 252.
One way to approach this problem is by using trial and error. We can start by squaring small integers and compare the results with 252. However, this method can be time-consuming and inefficient. Instead, we can use a more systematic approach to find the perfect square of 252.
First, we need to determine the square root of 252. The square root of a number is the value that, when multiplied by itself, gives the original number. To find the square root of 252, we can use a calculator or estimate it by considering the closest perfect squares around 252.
The closest perfect squares to 252 are 16 (4^2) and 25 (5^2). Since 252 is closer to 25 than 16, we can estimate that the square root of 252 is between 4 and 5. To find the exact value, we can use a calculator or perform long division.
After finding the square root of 252, we will have two possible integers: 4 and 5. To determine which one is the correct answer, we need to square each integer and compare the results with 252.
4^2 = 16
5^2 = 25
Since neither 16 nor 25 is equal to 252, we can conclude that 252 is not a perfect square. However, we can still find the perfect square closest to 252 by squaring the integer with the smaller absolute difference from the square root of 252.
The absolute difference between 4 and the square root of 252 is 2.5, while the absolute difference between 5 and the square root of 252 is 2.4. Therefore, 5 is the integer with the smaller absolute difference, and its square will be the perfect square closest to 252.
5^2 = 25
In conclusion, the perfect square closest to 252 is 25, which is the square of 5. Although 252 itself is not a perfect square, this exercise demonstrates the process of finding the perfect square of a given number and highlights the importance of understanding square roots in mathematics.
