SOLUTION: Alrighty, here is the question, 6 _____ 3+ sqrt 5 , I know that you have to use the conjugates when the same # with the different sign in the mid

Algebra ->  Algebra  -> Radicals -> SOLUTION: Alrighty, here is the question, 6 _____ 3+ sqrt 5 , I know that you have to use the conjugates when the same # with the different sign in the mid      Log On

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Question 97111This question is from textbook precalculus graphs and models
: Alrighty, here is the question,
6
_____
3+ sqrt 5 , I know that you have to use the conjugates when the same # with the different sign in the middle, so it should then look like this
6 3-sqrt5 18 +6sqrt 5
__________*______ =
3+sqrt 5 3-sqrt 5
then I think you foil the denominator, and get (3+sqrt5)(3-sqrt5), and this = to 9+3-sqrt5+3+sqrt5, and sqrt -5 and sqrt 5=-25, =-5and the middle cancels out and leaves you with 9-5=4 but the answer in the back of book is 9-3sqrt5
_______
2
how did they get that? thank you for your time. Stacy
_____This question is from textbook precalculus graphs and models

Answer by jim_thompson5910(21667) About Me  (Show Source):
You can put this solution on YOUR website!
I'm assuming you want to rationalize the denominator right?


6%2F%283%2Bsqrt%285%29%29 Start with the given expression


%286%2F%283%2Bsqrt%285%29%29%29%28%283-sqrt%285%29%29%2F%283-sqrt%285%29%29%29 Multiply the fraction by %283-sqrt%285%29%29%2F%283-sqrt%285%29%29


6%283-sqrt%285%29%29%2F%283%2Bsqrt%285%29%29%283-sqrt%285%29%29 Combine the fractions


6%283-sqrt%285%29%29%2F%283%2A3-3%2Asqrt%285%29%2B3sqrt%285%29-sqrt%285%29%2Asqrt%285%29%29 Foil


6%283-sqrt%285%29%29%2F%283%2A3%2Bcross%28-3%2Asqrt%285%29%2B3sqrt%285%29%29-sqrt%285%29%2Asqrt%285%29%29 Combine and cancel out like terms

6%283-sqrt%285%29%29%2F%289-5%29 Multiply


6%283-sqrt%285%29%29%2F4 Combine like terms


3%283-sqrt%285%29%29%2F2 Reduce 6%2F4 to 3%2F2 (this is probably where you got lost. You should have reduced before you distributed.)


%289-3%2Asqrt%285%29%29%2F2 Distribute




Check:

Plug in the expression 6%2F%283%2Bsqrt%285%29%29 into your calculator to approximately get 1.14589803375031


Now plug in %289-3%2Asqrt%285%29%29%2F2 into your calculator to approximately get 1.14589803375031

Since they are equivalent, (ie 6%2F%283%2Bsqrt%285%29%29=%289-3%2Asqrt%285%29%29%2F2) this verifies our answer