SOLUTION: <pre><b> __ __ <font face = "symbol">Ö</font>32 + <font face = "symbol">Ö</font>72</pre></b>

 __    __ 
Ö32 + Ö72

Break 32 and 72 into prime factors

32 = 8·4 = 4·2·2·2 = 2·2·2·2·2

72 = 8·9 = 4·2·3·3 = 2·2·2·3·3
 _________    _________
Ö2·2·2·2·2 + Ö2·2·2·3·3

Separate into group of 2 like factors since the index is 2.

 _____________    _____________
Ö(2·2)·(2·2)·2 + Ö(2·2)·2·(3·3)

Each pair of like factors comes out of the radical as a single
factor, and the unpaired number stays under the radical
    _       _
2·2Ö2 + 2·3Ö2
    _     _
  4Ö2 + 6Ö2
            _
Factor out Ö2
   _
  Ö2(4 + 6)
   _
  Ö2(10)
     _
  10Ö2

Edwin
AnlytcPhil@aol.com