SOLUTION: Simplify {{{sqrt(3)/sqrt(8)}}}

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Question 142360: Simplify sqrt%283%29%2Fsqrt%288%29
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%283%29%2Fsqrt%288%29 Start with the given expression


%28sqrt%283%29%2Fsqrt%288%29%29%28sqrt%288%29%2Fsqrt%288%29%29 Multiply both the numerator and denominator by sqrt%288%29


%28sqrt%283%29sqrt%288%29%29%2F%28sqrt%288%29sqrt%288%29%29 Combine the fractions



sqrt%283%2A8%29%2Fsqrt%288%2A8%29 Combine the square roots. Remember sqrt%28x%29%2Asqrt%28y%29=sqrt%28x%2Ay%29


sqrt%2824%29%2Fsqrt%2864%29 Multiply



sqrt%2824%29%2F8 Take the square root of 64 to get 8



sqrt%284%2A6%29%2F8 Factor 24 into 4*6


%28sqrt%284%29%2Asqrt%286%29%29%2F8 Break up the square roots using the identity sqrt%28x%2Ay%29=sqrt%28x%29%2Asqrt%28y%29


%282%2Asqrt%286%29%29%2F8 Take the square root of the perfect square 4 to get 2


%281%2Asqrt%286%29%29%2F4 Reduce 2%2F8 to get 1%2F4


sqrt%286%29%2F4 Simplify



So the expression sqrt%283%29%2Fsqrt%288%29 simplifies to sqrt%286%29%2F4