SOLUTION: sqrt of 2 divided by sqrt of 6- sqrt of 3 i know to take the exponent 2 so that i will have sqrt2 * sqrt 6 - sqrt 3 divided by 3... then i don't know...

Algebra ->  Rational-functions -> SOLUTION: sqrt of 2 divided by sqrt of 6- sqrt of 3 i know to take the exponent 2 so that i will have sqrt2 * sqrt 6 - sqrt 3 divided by 3... then i don't know...      Log On


   

Question 151056: sqrt of 2 divided by sqrt of 6- sqrt of 3
i know to take the exponent 2 so that i will have sqrt2 * sqrt 6 - sqrt 3 divided by 3... then i don't know...
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%28sqrt%282%29%29%2F%28sqrt%286%29-sqrt%283%29%29 Start with the given expression.


Take note that the conjugate of the denominator sqrt%286%29-sqrt%283%29 is sqrt%286%29%2Bsqrt%283%29. If we multiply the fraction by %28sqrt%286%29%2Bsqrt%283%29%29%2F%28sqrt%286%29%2Bsqrt%283%29%29, this will eliminate the square roots in the denominator



Multiply the fraction by %28sqrt%286%29%2Bsqrt%283%29%29%2F%28sqrt%286%29%2Bsqrt%283%29%29


Combine the fractions.


%28%28sqrt%282%29%29%28sqrt%286%29%2Bsqrt%283%29%29%29%2F%283%29 Foil the denominator to get


%28sqrt%282%29sqrt%286%29%2Bsqrt%282%29sqrt%283%29%29%2F%283%29 Distribute


%28sqrt%2812%29%2Bsqrt%286%29%29%2F%283%29 Combine and multiply the square roots.


%282%2Asqrt%283%29%2Bsqrt%286%29%29%2F%283%29 Simplify the square root.



So after rationalizing the denominator, the expression %28sqrt%282%29%29%2F%28sqrt%286%29-sqrt%283%29%29 simplifies to %282%2Asqrt%283%29%2Bsqrt%286%29%29%2F%283%29



In other words,