Is 980 a perfect square? This question often arises when people encounter the number 980 and wonder if it can be expressed as the square of an integer. In this article, we will explore the nature of 980 and determine whether it is indeed a perfect square.
The concept of a perfect square is rooted in the definition of a square number. A square number is an integer that can be expressed as the product of an integer with itself. For example, 1, 4, 9, 16, and 25 are all perfect squares because they can be obtained by squaring the integers 1, 2, 3, 4, and 5, respectively.
To determine if 980 is a perfect square, we need to find an integer that, when squared, equals 980. One way to do this is by taking the square root of 980 and checking if the result is an integer. The square root of 980 is approximately 31.516. Since 31.516 is not an integer, we can conclude that 980 is not a perfect square.
However, it is worth noting that 980 is a composite number, meaning it has factors other than 1 and itself. To further understand the factors of 980, we can perform prime factorization. The prime factorization of 980 is 2^2 × 5 × 7^2. This decomposition reveals that 980 has three distinct prime factors: 2, 5, and 7.
Now, let’s consider the possible combinations of these prime factors to form perfect squares. A perfect square can be formed by multiplying the same prime factors together. In the case of 980, we can see that the prime factors 2 and 7 can be squared to form 4 and 49, respectively. However, the prime factor 5 cannot be squared to form a perfect square since it is not a perfect square itself.
In conclusion, 980 is not a perfect square because it cannot be expressed as the square of an integer. While it is a composite number with prime factors 2, 5, and 7, these factors cannot be combined to form a perfect square. This article has shed light on the nature of 980 and its relationship to perfect squares.
