Is 175 a perfect square? This question often arises when people come across the number 175 and wonder if it can be expressed as the square of an integer. In this article, we will explore the nature of 175 and determine whether it is indeed a perfect square or not.
The concept of a perfect square is quite straightforward. A perfect square is a number that can be expressed as the square of an integer. For example, 16 is a perfect square because it is the square of 4 (4^2 = 16). On the other hand, 17 is not a perfect square because there is no integer that, when squared, equals 17.
To determine if 175 is a perfect square, we need to find an integer that, when squared, equals 175. One way to do this is by finding the square root of 175 and checking if it is an integer. The square root of 175 is approximately 13.23. Since 13.23 is not an integer, we can conclude that 175 is not a perfect square.
Another method to verify this is by checking the prime factors of 175. If a number has an odd number of prime factors, it cannot be a perfect square. The prime factors of 175 are 5 and 7, each occurring once. Since there are no repeated prime factors, 175 cannot be expressed as the square of an integer.
In conclusion, 175 is not a perfect square. This number does not have an integer square root and its prime factors do not allow it to be expressed as the square of an integer. Understanding the properties of perfect squares can help us identify and differentiate between numbers that are and are not perfect squares.
