Is 122 a perfect square? This question often arises when people encounter the number 122 in various mathematical contexts. In order to answer this question, we need to understand the concept of a perfect square and apply it to the number 122.
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 obtained by squaring the integers 1, 2, 3, 4, and 5, respectively. To determine if 122 is a perfect square, we need to find an integer whose square is equal to 122.
One way to check if a number is a perfect square is to calculate its square root and see if it is an integer. The square root of 122 is approximately 11.0905. Since this value is not an integer, we can conclude that 122 is not a perfect square.
Another method to determine if a number is a perfect square is to look for patterns in its prime factorization. A perfect square will have an even number of each prime factor in its factorization. For instance, the prime factorization of 16 is 2^4, which indicates that 16 is a perfect square. However, the prime factorization of 122 is 2 61, meaning it has an odd number of prime factors, which confirms that 122 is not a perfect square.
In conclusion, 122 is not a perfect square because its square root is not an integer, and its prime factorization does not exhibit the even distribution of prime factors that characterize perfect squares. Understanding the properties of perfect squares can help us identify and differentiate between perfect and non-perfect squares in various mathematical scenarios.
