What is the perfect square of 225? This question often arises when dealing with square numbers and their properties. In this article, we will explore the concept of perfect squares, how to identify them, and determine the perfect square of 225.
A perfect square is a number that can be expressed as the square of an integer. In other words, it is the product of a number multiplied by itself. For example, 4 is a perfect square because it can be written as 2 multiplied by 2 (2 x 2 = 4). Similarly, 9 is a perfect square because it is the square of 3 (3 x 3 = 9).
To find the perfect square of 225, we need to determine the integer that, when squared, equals 225. One way to do this is by using the prime factorization method. Prime factorization involves breaking down a number into its prime factors, which are numbers that cannot be divided further without resulting in a non-integer value.
Let’s begin by finding the prime factors of 225:
225 = 3 x 75
75 = 3 x 25
25 = 5 x 5
Now, we have the prime factorization of 225: 3 x 3 x 5 x 5. To find the perfect square, we need to pair up the prime factors in groups of two. In this case, we have two pairs of 3s and two pairs of 5s:
(3 x 3) x (5 x 5) = 9 x 25
Now, we can square the numbers in each pair:
9^2 = 81
25^2 = 625
Finally, we multiply the squared numbers together to find the perfect square of 225:
81 x 625 = 50625
Therefore, the perfect square of 225 is 50625. This means that 225 can be expressed as the square of 225, which is (225)^2 = 50625. Understanding the concept of perfect squares and how to find them can be beneficial in various mathematical applications, such as algebra, geometry, and number theory.
