Hey guys,
I don't really understand the bold part of the answer below. Can anyone please explain!
Question:
x is divisible by 144. If ³√x is an integer, then which of the following
is ³√x definitely divisible by? (Choose all that apply)
Answer:
Remember that when we complete a prime box for a variable, that
variable could still have additional factors. 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 (3, 6, 9, etc.). In this case, that
means the factors of x that we can’t see must include at least two
additional 2s and one additional 3. From this information, we can
definitively conclude that ³√x must have two 2s and one 3 as
factors. 4 and 12 are the only numbers in the list we can guarantee
are factors of ³√x .
I don't really understand the bold part of the answer below. Can anyone please explain!
Question:
x is divisible by 144. If ³√x is an integer, then which of the following
is ³√x definitely divisible by? (Choose all that apply)
Answer:
Remember that when we complete a prime box for a variable, that
variable could still have additional factors. 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 (3, 6, 9, etc.). In this case, that
means the factors of x that we can’t see must include at least two
additional 2s and one additional 3. From this information, we can
definitively conclude that ³√x must have two 2s and one 3 as
factors. 4 and 12 are the only numbers in the list we can guarantee
are factors of ³√x .
