SOLUTION: Rationalize the denominator: {{{5/(sqrt(3)+sqrt(5))}}}

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Question 147682: Rationalize the denominator:

5%2F%28sqrt%283%29%2Bsqrt%285%29%29
Answer by jim_thompson5910(21667) About Me  (Show Source):
You can put this solution on YOUR website!

5%2F%28sqrt%283%29%2Bsqrt%285%29%29 Start with the given expression.


%285%2F%28sqrt%283%29%2Bsqrt%285%29%29%29%28%28sqrt%283%29-sqrt%285%29%29%2F%28sqrt%283%29-sqrt%285%29%29%29 Multiply both the numerator and denominator by the conjugate of the denominator sqrt%283%29-sqrt%285%29.


%285%28sqrt%283%29-sqrt%285%29%29%29%2F%28%28sqrt%283%29%2Bsqrt%285%29%29%28sqrt%283%29-sqrt%285%29%29%29 Combine the fractions.


%285%28sqrt%283%29-sqrt%285%29%29%29%2F%283-5%29 Foil the denominator.


%285%28sqrt%283%29-sqrt%285%29%29%29%2F%28-2%29 Combine like terms.


%285%2Asqrt%283%29-5%2Asqrt%285%29%29%2F%28-2%29 Distribute.


So 5%2F%28sqrt%283%29%2Bsqrt%285%29%29 simplifies to %285%2Asqrt%283%29-5%2Asqrt%285%29%29%2F%28-2%29


In other words, 5%2F%28sqrt%283%29%2Bsqrt%285%29%29=%285%2Asqrt%283%29-5%2Asqrt%285%29%29%2F%28-2%29