SOLUTION: √33/√77 Rationalize the denominator and simplify:

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Question 185800: √33/√77

Rationalize the denominator and simplify:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%2833%29%2Fsqrt%2877%29 Start with the given expression


%28sqrt%2833%29%2Asqrt%2877%29%29%2F%28sqrt%2877%29%2Asqrt%2877%29%29 Multiply both the numerator and denominator by sqrt%2877%29


%28sqrt%2833%29%2Asqrt%2877%29%29%2F%2877%29 Multiply sqrt%2877%29 by sqrt%2877%29 to get 77


%28sqrt%283%2A11%29%2Asqrt%2811%2A7%29%29%2F%2877%29 Factor 33 into 3*11 and factor 77 into 11*7


%28sqrt%283%2A11%2A11%2A7%29%29%2F%2877%29 Combine the roots.


%28sqrt%283%2A11%5E2%2A7%29%29%2F%2877%29 Multiply


%28sqrt%283%29%2Asqrt%2811%5E2%29%2Asqrt%287%29%29%2F%2877%29 Break up the square root


%28sqrt%283%29%2A11%2Asqrt%287%29%29%2F%2877%29 Take the square root of 11%5E2 to get 11


%2811%2Asqrt%283%2A7%29%29%2F%2877%29 Recombine the square roots.


%2811%2Asqrt%2821%29%29%2F%2877%29 Multiply


%2811%2Asqrt%2821%29%29%2F%287%2A11%29 Factor 77 into 7*11


%28cross%2811%29%2Asqrt%2821%29%29%2F%287%2Across%2811%29%29 Cancel out the common terms.


sqrt%2821%29%2F7 Simplify


So sqrt%2833%29%2Fsqrt%2877%29=sqrt%2821%29%2F7