Question 25298
<pre><font size = 4><b> __    __ 
<font face = "symbol">Ö</font>32 + <font face = "symbol">Ö</font>72

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
 _________    _________
<font face = "symbol">Ö</font>2·2·2·2·2 + <font face = "symbol">Ö</font>2·2·2·3·3

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

 _____________    _____________
<font face = "symbol">Ö</font>(2·2)·(2·2)·2 + <font face = "symbol">Ö</font>(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
    _       _
2·2<font face = "symbol">Ö</font>2 + 2·3<font face = "symbol">Ö</font>2
    _     _
  4<font face = "symbol">Ö</font>2 + 6<font face = "symbol">Ö</font>2
            _
Factor out <font face = "symbol">Ö</font>2
   _
  <font face = "symbol">Ö</font>2(4 + 6)
   _
  <font face = "symbol">Ö</font>2(10)
     _
  10<font face = "symbol">Ö</font>2

Edwin
AnlytcPhil@aol.com</pre></b>