Is 245 a perfect square? This question often arises when people encounter the number 245 and wonder if it can be expressed as the square of an integer. In this article, we will explore the nature of 245 and determine whether it is indeed a perfect square or not.
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). To determine if 245 is a perfect square, we need to find an integer that, when squared, equals 245.
To do this, we can start by finding the square root of 245. 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 multiplied by itself, equals 245.
The square root of 245 is approximately 15.65. Since the square root of 245 is not a whole number, we can conclude that 245 is not a perfect square. Instead, it is a composite number, meaning it has factors other than 1 and itself.
To further illustrate this, let’s factorize 245. We can start by dividing 245 by the smallest prime number, which is 2. 245 divided by 2 is 122.5, which is not an integer. Therefore, 2 is not a factor of 245.
Next, we move on to the next prime number, which is 3. 245 divided by 3 is approximately 81.6667, which is also not an integer. Thus, 3 is not a factor of 245.
We continue this process with the next prime numbers, 5, 7, and 11. None of these prime numbers divide 245 evenly, indicating that 245 does not have any prime factors other than 1 and itself.
In conclusion, 245 is not a perfect square because it cannot be expressed as the square of an integer. Instead, it is a composite number with no prime factors other than 1 and itself. This demonstrates the importance of understanding the properties of numbers and their factors in mathematics.
