SOLUTION: rationalize the denominator for the expression square root 5 + square root of 55 all over the square root of 5

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Question 84046: rationalize the denominator for the expression square root 5 + square root of 55 all over the square root of 5
Answer by jim_thompson5910(21667) About Me  (Show Source):
You can put this solution on YOUR website!
%28sqrt%285%29%2Bsqrt%2855%29%29%2F%28sqrt%285%29%29 Start with the given expression

%28%28sqrt%285%29%2Bsqrt%2855%29%29%2F%28sqrt%285%29%29%29%28%28sqrt%285%29%29%2F%28sqrt%285%29%29%29 Multiply both numerator and denominator by sqrt%285%29 to rationalize the denominator

%28sqrt%285%29sqrt%285%29%2Bsqrt%285%29sqrt%2855%29%29%2F%28sqrt%285%29sqrt%285%29%29 Distribute

%28sqrt%285%2A5%29%2Bsqrt%285%2A55%29%29%2F%28sqrt%285%2A5%29%29 Combine the square roots

%28sqrt%2825%29%2Bsqrt%28275%29%29%2F%28sqrt%2825%29%29 Multiply

%285%2Bsqrt%28275%29%29%2F%285%29 Take the square root of any perfect squares

%285%2Bsqrt%2825%2A11%29%29%2F%285%29 Factor 275 into 25*11

%285%2Bsqrt%2825%29%2Asqrt%2811%29%29%2F%285%29 Break apart the square roots

%285%2B5%2Asqrt%2811%29%29%2F%285%29 Take the square root of 25

5%281%2Bsqrt%2811%29%29%2F%285%29 Factor out a 5 out of the numerator

cross%285%29%281%2Bsqrt%2811%29%29%2Fcross%285%29 Divide

So the expression simplifies to

1%2Bsqrt%2811%29