What is the perfect square of 144? This question may seem simple at first glance, but it actually leads to an intriguing exploration of mathematics. In this article, we will delve into the concept of perfect squares, the properties of 144, and how they relate to each other.
In mathematics, 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 1^2, 2^2, 3^2, 4^2, and 5^2, respectively. The perfect square of a number is always non-negative, and it represents the area of a square with side lengths equal to the square root of the number.
Now, let’s address the question at hand: what is the perfect square of 144? To find the answer, we need to determine the square root of 144. The square root of a number is the value that, when multiplied by itself, gives the original number. In this case, we are looking for a number that, when squared, equals 144.
To calculate the square root of 144, we can use the prime factorization method. First, we need to factorize 144 into its prime factors. The prime factorization of 144 is:
144 = 2 × 2 × 2 × 2 × 3 × 3
Now, we can group the prime factors into pairs, as each pair represents a factor that, when squared, will give us a perfect square:
144 = (2 × 2) × (2 × 2) × 3 × 3
Simplifying further, we get:
144 = 4 × 4 × 3 × 3
From this grouping, we can see that the square root of 144 is 12, since 12 × 12 = 144. Therefore, the perfect square of 144 is 12^2, which is equal to 144.
In conclusion, the perfect square of 144 is 144 itself, as it is the square of 12. This example highlights the beauty and simplicity of mathematics, as well as the importance of understanding the properties of numbers and their relationships. By exploring the concept of perfect squares and their applications, we can appreciate the wonders of mathematics and its endless possibilities.
