Stanbon's solution to your problem is incorrect.

Simplify and ractionalize all denominators:

 

There are no denominators to rationalize, so we just simplify this one

Break up what's under the radicals completely into prime factors:

Break up  into primes as 

Break up  into primes 

Substitute these under the radicals:

 + 

Since the index of the root is 2 (square root) we group all
like factors by twos (pairs) that we can like this.  We will
often have factors left over that would not pair up:

 + 

Each pair of like factors can be written as a square

 + 

Take out each square from under the radical out front of the radical,
like this, leaving what didn't pair up under the radical:

 + 

Simplify what's in front of the radicals:

 + 

Now you can factor out GCF = 

( + )





Edwin