How Do We Approach This Problem?
To begin, what is a square number? Well, a square number is any number formed when another number is multiplied by itself. For instance, 16 is a square or a perfect square because it can be represented as 4 x 4. So, what do you think is the smallest square number? Believe it or not, but 1 is the smallest because it can be expressed as 1 x 1. Regardless, how exactly do we approach this problem? First, let me ask you a question. What is the smallest number that will ensure that 20 times that value is a square number? Of course, this has to be 5. Now, this was a relatively small value, which made it pretty easy to find the answer. However, what is actually going on behind the scenes? Have you ever heard of the term prime factorization? Very simply put, this is the breakdown of a value using something called prime numbers. In case you didn’t know, prime numbers are values that can only be divided by 1 and themselves. For example, 2, 3, 11, and 23 are all prime numbers. By the way, I have created a great app for prime numbers on the App Store: Prime #’s….
Anyways, when we look at the number 20, we realize that it can be broken down into 2 x 2 x 5. This is the prime factorization of 20. Let’s also remember that a square number n can be represented by y * y. Thus, we have found a pattern.
Let’s Solve The Problem Together:
Correspondingly, we will first find the prime factorization of 1452. I will use my app to do so: We then get 2^2 x 3 x 11^2. With this in mind, we can easily figure out that to make the product of 1452 and another value v, the smallest possible value for v will be 3. This will then give us a product of 4,356, which is the same (2x3x11)^2 or 66 squared. In conclusion, because of the reasons listed above, the smallest possible value for v in 1452*v to make the product a square number will be 3. Not to mention, it is incredible how we turned this extremely difficult problem into something much easier!
