SOLUTION: I am completely lost Rationalize the Denominator 2/"square root of 6" - "square root of 5" Thank you very much for your help.

Algebra ->  Algebra  -> Radicals -> SOLUTION: I am completely lost Rationalize the Denominator 2/"square root of 6" - "square root of 5" Thank you very much for your help.       Log On

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Question 118145: I am completely lost
Rationalize the Denominator
2/"square root of 6" - "square root of 5"
Thank you very much for your help.

Answer by jim_thompson5910(21667) About Me  (Show Source):
You can put this solution on YOUR website!

%282%29%2F%28sqrt%286%29-sqrt%285%29%29 Start with the given expression


%28%282%29%2F%28sqrt%286%29-sqrt%285%29%29%29%28%28sqrt%286%29%2Bsqrt%285%29%29%2F%28sqrt%286%29%2Bsqrt%285%29%29%29 Multiply by the fraction by %28sqrt%286%29%2Bsqrt%285%29%29%2F%28sqrt%286%29%2Bsqrt%285%29%29. Note sqrt%286%29%2Bsqrt%285%29 is the conjugate of sqrt%286%29-sqrt%285%29.


%28%282%29%28sqrt%286%29%2Bsqrt%285%29%29%29%2F%28%28sqrt%286%29-sqrt%285%29%29%28sqrt%286%29%2Bsqrt%285%29%29%29 Combine the fractions


%282%29%28sqrt%286%29%2Bsqrt%285%29%29%2F%28sqrt%286%29%2Asqrt%286%29%2B%28sqrt%286%29%29%28sqrt%285%29%29-sqrt%286%29sqrt%285%29%2B%28-sqrt%285%29%29%2A%28-sqrt%285%29%29%29 Foil the denominator


%282%29%28sqrt%286%29%2Bsqrt%285%29%29%2F%28sqrt%286%29%2Asqrt%286%29%2B%28-sqrt%285%29%29%2A%28-sqrt%285%29%29%29 Cancel like terms


%28%282%29%28sqrt%286%29%2Bsqrt%285%29%29%29%2F%286-5%29 Multiply

%28%282%29%28sqrt%286%29%2Bsqrt%285%29%29%29%2F%281%29 Combine like terms


%282%29%28sqrt%286%29%2Bsqrt%285%29%29 Remove the denominator of 1


2%2Asqrt%286%29%2B2%2Asqrt%285%29 Distribute