Square root 8 + Square root 18
   _    __
  Ö8 + Ö18

Break 8 into prime factors: 8 = 2·4 = 2·2·2

Break 18 into prime factors: 18 = 2·9 = 2·3·3
  _____    _____
 Ö2·2·2 + Ö2·3·3

Since it is a square root, use parentheses to group like factors
into groups of 2. (If it were a cube root you would group by three
like factors, fourth root -- group by fours, etc.

  _______    _______
 Ö(2·2)·2 + Ö2·(3·3)

Each group of factors under the radical comes outside the radical
as a single factor.  That is, the (2·2) under the first radical
comes out front as a single 2.  The (3·3) under the second radical
comes out front as a single 3.  The 2's that did not pair up must
stay under the radical.  So we have
   _      _
2·Ö2 + 3·Ö2
                       _
Now we factor out the Ö2 and get
 _
Ö2·(2 + 3)
 _
Ö2·(5)
   _
5·Ö2

Edwin
AnlytcPhil@aol.com