SOLUTION: can you please help me express in simplest radical form:((( (square root sign3 - square root sign5)(square root sign3 - square root sign5) )))

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Question 178941This question is from textbook algebra structure and method
: can you please help me express in simplest radical form:((( (square root sign3 - square root sign5)(square root sign3 - square root sign5) ))) This question is from textbook algebra structure and method

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%28sqrt%283%29-sqrt%285%29%29%28sqrt%283%29-sqrt%285%29%29 Start with the given expression


Let a=sqrt%283%29 and b=sqrt%285%29


%28a-b%29%28a-b%29 Replace each sqrt%283%29 with "a" and each sqrt%285%29 with "b"


a%5E2-ab-ab%2Bb%5E2 FOIL


a%5E2-2ab%2Bb%5E2 Combine like terms.


a%5E2-2ab%2Bb%5E2 Combine like terms.


%28sqrt%283%29%29%5E2-2%2Asqrt%283%29%2Asqrt%285%29%2B%28sqrt%285%29%29%5E2 Plug in a=sqrt%283%29 and b=sqrt%285%29


%28sqrt%283%29%29%5E2-2%2Asqrt%2815%29%2B%28sqrt%285%29%29%5E2 Multiply and combine the radicals


3-2%2Asqrt%2815%29%2B5 Square sqrt%283%29 to get 3 and square sqrt%285%29 to get 5


8-2%2Asqrt%2815%29 Combine like terms.


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Answer:


So %28sqrt%283%29-sqrt%285%29%29%28sqrt%283%29-sqrt%285%29%29=8-2%2Asqrt%2815%29