Is 125 a perfect cube? This question may seem simple at first glance, but it can lead to an interesting exploration of mathematics. In this article, we will delve into the concept of perfect cubes and determine whether 125 fits the criteria.
A perfect cube is a number that can be expressed as the cube of an integer. For example, 8 is a perfect cube because it is equal to 2^3 (2 multiplied by itself three times). To determine if 125 is a perfect cube, we need to find an integer whose cube is equal to 125.
To do this, we can start by looking at the prime factorization of 125. Prime factorization involves breaking down a number into its prime factors, which are numbers that cannot be divided further. The prime factorization of 125 is 5 x 5 x 5, or 5^3.
Since the prime factorization of 125 consists of only one prime number, 5, and it is raised to the power of 3, we can conclude that 125 is a perfect cube. The integer whose cube is 125 is 5, as 5^3 equals 125.
In summary, 125 is indeed a perfect cube. This example highlights the importance of prime factorization in determining whether a number is a perfect cube. By breaking down a number into its prime factors, we can easily identify whether it is a perfect cube or not.
