Hi guys, I dont really understand how Greg got to the steps after prime factoring 24 and 108. If anyone could help me understand the steps that would be great bc im really lost.
The first picture is what Ihe did and the second one what I did.
He prime factored those numbers to find their LCM. This matters, since by picking some ginormous multiple of 24 and 108, we would think all the answers work. If we find the smallest possible workable number for n^2 we can potentially rule out some choices.
The LCM is 216, so we can prime factor it to 2^3 * 3^3, right? But n^2 can’t be 2^3 * 3^3 – since you can’t square an integer and get something to the 3rd. N wouldn’t be an integer, which would break the rules of the question. So we need a bigger multiple of 24 and 108, once that we can cleanly square root.
By using 2^4*3^4 for n^2, we can find the smallest multiple of 24 and 108 that lets n be an integer (2^2*3^2) - we need both prime factors to have even exponents to end up with an integer after taking the root.