Is 675 a perfect square? This question often arises when dealing with numbers and their properties. In this article, we will explore the concept of perfect squares and determine whether 675 fits the criteria.
A perfect square is a number that can be expressed as the square of an integer. For example, 4 is a perfect square because it is the square of 2 (2^2 = 4). Similarly, 9 is a perfect square because it is the square of 3 (3^2 = 9). To determine if a number is a perfect square, we need to find its square root and check if it is an integer.
Let’s analyze the number 675. To do this, we will find its square root. The square root of a number is the value that, when multiplied by itself, gives the original number. In the case of 675, we need to find a number that, when squared, equals 675.
Using a calculator or by estimation, we find that the square root of 675 is approximately 25.98. Since this value is not an integer, we can conclude that 675 is not a perfect square. However, this is not the end of our exploration.
Now, let’s delve deeper into the factors of 675. To determine if a number is a perfect square, we must consider its prime factors. Prime factors are the prime numbers that, when multiplied together, give the original number. In the case of 675, we need to find its prime factors to determine if it can be expressed as a perfect square.
The prime factorization of 675 is as follows: 675 = 3^3 5^2. This means that 675 can be expressed as the product of three 3’s and two 5’s. Since the prime factorization of a perfect square consists of pairs of prime factors, we can conclude that 675 is not a perfect square because it has an odd number of 3’s and an even number of 5’s.
In conclusion, after analyzing the prime factors and square root of 675, we can confidently say that 675 is not a perfect square. This number can be expressed as the product of its prime factors, but it does not have the necessary pairings to be considered a perfect square. Understanding the properties of perfect squares and their prime factors can help us determine whether a given number is a perfect square or not.
