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Here's another one:

5 / sqrt(10) = ( 5 / sqrt(10) )( sqrt(10)*sqrt(10) ) = ( 5*sqrt(10) / sqrt(100) ) = ( 5*sqrt(10) / 10 ) = sqrt(10) / 2     reduce 5/10 = 1/2


YOUR TURN:

Rationalize the denominator: 

6 / sqrt(15)


They get messier...

What if we needed to get the radical out of this denominator?

5 / ( 2 - sqrt(3) )

Same game -- we still multiply by a magic 1...

06-Radicals-08.gif
The magic 1 will be made up of this guy's conjugate.

Well now, that was helpful wasn't it?

Conjugate = same guy, different sign

So, the conjugate of

2 - sqrt(3)   is   2 + sqrt(3)