SOLUTION: Can you please help me simplify this equation using radicals? I believe you must use a conjugate. 3+the square root of 7/1-the square root of 3.

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Question 117919: Can you please help me simplify this equation using radicals? I believe you must use a conjugate. 3+the square root of 7/1-the square root of 3.

Answer by jim_thompson5910(21685) About Me  (Show Source):
You can put this solution on YOUR website!
%283%2Bsqrt%287%29%29%2F%281-sqrt%283%29%29 Start with the given expression


%28%283%2Bsqrt%287%29%29%2F%281-sqrt%283%29%29%29%28%281%2Bsqrt%283%29%29%2F%281%2Bsqrt%283%29%29%29 Multiply by the fraction by %281%2Bsqrt%283%29%29%2F%281%2Bsqrt%283%29%29. Note 1%2Bsqrt%283%29 is the conjugate of 1-sqrt%283%29.


%28%283%2Bsqrt%287%29%29%281%2Bsqrt%283%29%29%29%2F%28%281-sqrt%283%29%29%281%2Bsqrt%283%29%29%29 Combine the fractions


%28%283%2Bsqrt%287%29%29%281%2Bsqrt%283%29%29%29%2F%281%2A1%2B1%28-sqrt%283%29%29-%28-sqrt%283%29%29%2A1%2B%28-sqrt%283%29%29%28-sqrt%283%29%29%29 Foil the denominator


%28%283%2Bsqrt%287%29%29%281%2Bsqrt%283%29%29%29%2F%281%2A1%2B%28-sqrt%283%29%29%28-sqrt%283%29%29%29 Cancel like terms


%28%283%2Bsqrt%287%29%29%281%2Bsqrt%283%29%29%29%2F%281-3%29 Multiply


%28%283%2Bsqrt%287%29%29%281%2Bsqrt%283%29%29%29%2F%28-2%29 Combine like terms



%28%283%29%281%29%2B%283%29%28sqrt%283%29%29%2B%28sqrt%287%29%29%281%29%2B%28sqrt%287%29%29%28sqrt%283%29%29%29%2F%28-2%29 Foil the numerator



%283%2B3sqrt%283%29%2Bsqrt%287%29%2Bsqrt%2821%29%29%2F%28-2%29 Multiply