simplify the expression: cubed root of 648

Question

michele_laino · Answer

please note that:
$$648=8*81=2^{3}*3^{3}$$

mathstudent55 · Answer

The first step is to find the prime factorization of 648.
Do you know how to do that?

anonymous · Answer

mathstudent 55 no I do not know how to do that

mathstudent55 · Answer

Then here goes.
First, familiarize yourself with a list of the first 10 or 15 prime numbers.
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, ...

mathstudent55 · Answer

To find the prime factors of a number start by dividing the number by the smallest prime number it is divisible by. Then keep dividing by that p[rime until it is no longer divisible. Then move on tot he next prime and do the same. In the end, you must end up with 1.

mathstudent55 · Answer

I'll show you an example using the number 630.
Let's find the prime factorization of 630.

mathstudent55 · Answer

Set it up like this:
|dw:1418574164902:dw|

mathstudent55 · Answer

Now remember the prime numbers.
We start with  the smallest prime, 2.
630 is divisible by 2, so we divide 630 by 2 to get 315 and write it like this:
|dw:1418574240763:dw|