SOLUTION: Rationalize the denominator: 2____ √[3] + √[2]

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Question 132680: Rationalize the denominator:
2____
√[3] + √[2]
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%282%29%2F%28sqrt%282%29%2Bsqrt%283%29%29 Start with the given expression


Multiply by the fraction by %28sqrt%282%29-sqrt%283%29%29%2F%28sqrt%282%29-sqrt%283%29%29. Note sqrt%282%29-sqrt%283%29 is the conjugate of sqrt%282%29%2Bsqrt%283%29.


Combine the fractions


Foil the denominator


Cancel like terms


%28%282%29%28sqrt%282%29-sqrt%283%29%29%29%2F%282-3%29 Multiply


%28%282%29%28sqrt%282%29-sqrt%283%29%29%29%2F%28-1%29 Combine like terms


-2%28sqrt%282%29-sqrt%283%29%29 Divide and simplify


-2sqrt%282%29%2B2sqrt%283%29 Distribute


So %282%29%2F%28sqrt%282%29%2Bsqrt%283%29%29 simplifies to -2sqrt%282%29%2B2sqrt%283%29



In other words, %282%29%2F%28sqrt%282%29%2Bsqrt%283%29%29=-2sqrt%282%29%2B2sqrt%283%29