SOLUTION: <pre><b><font size = 2><b>add and/or subtract and simplify the following radical expression. __ __ __ 3<font face = "symbol">Ö</font>48 - 2<font face = "symbol">Ö</fon

add and/or subtract and simplify the following radical expression. 
  __     __     __
3Ö48 - 2Ö27 - 3Ö12

thanks for your time
  __     __     __
3Ö48 - 2Ö27 - 3Ö12

Break 48 down into primes: 48 = 8·6 = 4·2·2·3 = 2·2·2·2·3

Break 27 down into primes: 27 = 3·9 = 3·3·3

Break 12 down into primes: 12 = 4·3 = 2·2·3

Replace the radicands by their prime factorizations:
  _________     _____     _____
3Ö2·2·2·2·3 - 2Ö3·3·3 - 3Ö2·2·3

Now group the factors under the radicals into pairs
of like factors as much as possible. (Note: if these
had been cube roots you would have grouped by threes
instead of by twos, and if they had been fourth roots
you would have grouped by fours, etc.)

  _____________     _______     _______
3Ö(2·2)·(2·2)·3 - 2Ö(3·3)·3 - 3Ö(2·2)·3

Now each pair is a square and will come out in front of the radical
as a SINGLE factor.

Each of the (2·2)'s comes out in front of of the 1st and 3rd radicals
as a SINGLE 2 factor. 

The (3·3) comes out of the 2nd radical as a SINGLE 3 factor.

So we have
      _       _       _
3·2·2Ö3 - 2·3Ö3 - 3·2Ö3

or
   _     _     _ 
12Ö3 - 6Ö3 - 6Ö3
            _
Factor out Ö3
 _
Ö3(12 - 6 - 6)
 _
Ö3(0)

  0 

The answer is 0.

Edwin McCravy
AnlytcPhil@aol.com