SOLUTION: I have done this chapter over completely 5 times now and still I am not getting the why of some of the things on radicals. I will send my questions in seperate emails but her is on

Algebra ->  Radicals -> SOLUTION: I have done this chapter over completely 5 times now and still I am not getting the why of some of the things on radicals. I will send my questions in seperate emails but her is on      Log On


   

Question 874543: I have done this chapter over completely 5 times now and still I am not getting the why of some of the things on radicals. I will send my questions in seperate emails but her is one problem (I'm teaching myself algebra so I have no teacher to ask):
Simplify:
radical 48 over radical 18
So I simplified by dividing by 6 which gave me radical 8 over radical 3
then I broke down radical 8 into radical (2*4)and left the radical 3 as it is
then I took the radical four and made it into a whole 2 with a radical 2 and placed it over the radical 3 as my answer.
However my book says that is wrong. In the back where the answers are it says when I got radical 8 over radical 3 I should have then multiplied radical 3 to both the numerator and denominator giving me radical 24 over the whole number 3
then break 24 down into radical (4*6) over 3 which then would have given me 2 radical 6 over 3.
Why should I have done the multiplying at that stage instead of breaking the 8 into radical (2*4)?
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
You want to factor out squares like 4 9 16 36
sqrt%2848%29%2Fsqrt%2818%29
sqrt%2816%2A3%29%2Fsqrt%282%2A9%29
4sqrt%283%29%2F3sqrt%282%29
4%2F3%2Asqrt%283%29%2Fsqrt%282%29
multiply by sqrt%282%29%2Fsqrt%282%29
4%2F3%2Asqrt2%2Asqrt%283%29%2Fsqrt%282%29sqrt%282%29
4%2F3%2Asqrt%286%29%2F2
2%2F3%2Asqrt%286%29