What is the perfect square of 125? This question might seem simple at first glance, but it holds a significant place in the realm of mathematics. In this article, we will delve into the concept of perfect squares and find the exact answer to this query.
A perfect square is a number that can be expressed as the square of an integer. For example, 1, 4, 9, 16, 25, and so on are all perfect squares because they can be written as the square of 1, 2, 3, 4, 5, and so forth, respectively. The square root of a perfect square is always an integer.
Now, let’s address the main question: What is the perfect square of 125? To find the answer, we need to determine the integer that, when squared, will yield 125. In other words, we are looking for an integer ‘n’ such that n^2 = 125.
To solve this equation, we can take the square root of both sides. This gives us:
√(n^2) = √125
Simplifying the left side, we get:
n = √125
To find the value of √125, we can break it down into its prime factors. The prime factorization of 125 is 5^3. Therefore, we have:
n = √(5^3)
Since we are looking for an integer value of ‘n’, we can take the cube root of 5 and then square it to find the value of ‘n’:
n = (5^(3/2))^2
n = 5^3
n = 125
Hence, the perfect square of 125 is 125 itself. This is because 125 is the square of 11 (11^2 = 125). Therefore, the answer to the question “What is the perfect square of 125?” is 125.
