X is divisible by 144. If the cubed root of X is an integer, then which of the following is the cubed root of x definitely divisible by? Choose all that apply.
a) 4
b) 8
c) 9
d) 12
Answer: 4 and 12
Prime factorization of 144: 2^4 * 3^2
The explanation for this problem says that in order for the cube root of a number to be an integer, the original number must have 3 of each prime factor or some multiple of 3. So, that means the factors of X that we can't see must include at least two additional 2's and one additional 3. That's what I don't understand. Why couldn't it be one additional 2 and two additional 3s? Can someone explain this to me pleaaase?
a) 4
b) 8
c) 9
d) 12
Answer: 4 and 12
Prime factorization of 144: 2^4 * 3^2
The explanation for this problem says that in order for the cube root of a number to be an integer, the original number must have 3 of each prime factor or some multiple of 3. So, that means the factors of X that we can't see must include at least two additional 2's and one additional 3. That's what I don't understand. Why couldn't it be one additional 2 and two additional 3s? Can someone explain this to me pleaaase?
