SOLUTION: rationalize the denominator: sqrt 2 divided by sqrt 6 - sqrt 3

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Question 151059: rationalize the denominator:
sqrt 2 divided by sqrt 6 - sqrt 3
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%28sqrt%282%29%29%2F%28sqrt%286%29-sqrt%283%29%29 Start with the given expression.


Take note that the conjugate of the denominator sqrt%286%29-sqrt%283%29 is sqrt%286%29%2Bsqrt%283%29. If we multiply the fraction by %28sqrt%286%29%2Bsqrt%283%29%29%2F%28sqrt%286%29%2Bsqrt%283%29%29, this will eliminate the square roots in the denominator



Multiply the fraction by %28sqrt%286%29%2Bsqrt%283%29%29%2F%28sqrt%286%29%2Bsqrt%283%29%29


Combine the fractions.


%28%28sqrt%282%29%29%28sqrt%286%29%2Bsqrt%283%29%29%29%2F%283%29 Foil the denominator to get


%28sqrt%282%29sqrt%286%29%2Bsqrt%282%29sqrt%283%29%29%2F%283%29 Distribute


%28sqrt%2812%29%2Bsqrt%286%29%29%2F%283%29 Combine and multiply the square roots.


%282%2Asqrt%283%29%2Bsqrt%286%29%29%2F%283%29 Simplify the square root.



So after rationalizing the denominator, the expression %28sqrt%282%29%29%2F%28sqrt%286%29-sqrt%283%29%29 simplifies to %282%2Asqrt%283%29%2Bsqrt%286%29%29%2F%283%29



In other words,