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Rationalizing Denominators

Check out how it works:

( 5 / ( 2 - sqrt(3) )( ( 2 + sqrt(3) ) / ( 2 + sqrt(3) )
Put ( ) around everyone or you're
really going to mess things up!

( 5 / ( 2 - sqrt(3) )( ( 2 + sqrt(3) ) / ( 2 + sqrt(3) ) = ( 10 + 5*sqrt(3) ) / ( 4 - sqrt(9) ) = ( 10 + 5*sqrt(3) ) / (4 - 3 ) = 10 + 5*sqrt(3)

Not only did we ditch the radical in the denominator,
in this one, we ditched the whole denominator.

Here's another one:

4 / ( 1 + sqrt(7) ) = ( 4 / ( 1 + sqrt(7) ) )( ( 1 - sqrt(7) ) / ( 1 - sqrt(7) ) ) = ( 4 - 4*sqrt(7) ) / ( 1 - sqrt(49) ) = ( 4 - 4*sqrt(7) ) / ( 1 - 7 ) = ( 4 - 4*sqrt(7) ) / ( -6 ) = ( -2( -2 + 2*sqrt(7) ) ) / ( -6 ) = ( -2 + 2*sqrt(7) ) / 3

TRY IT:

Rationalize the denominator:

3 / ( 2 - sqrt(6) )

answers