Question

multiply 2+root3*(3-root5)

Answer 1

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GMAT Club Forum Index  Problem Solving (PS)

sqrt(5)+sqrt(3)) / (sqrt(5)-sqrt(3)) = : Problem Solving (PS)

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Difficulty: 600-700 Level      

Topic Discussion

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chets

Sep 13, 2005





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100% (00:37) correct

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5√+3√5√−3√=5+35−3=

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duttsit

Sep 13, 2005

(sqrt(5)+sqrt(3)) / (sqrt(5)-sqrt(3)) 

multiple both numerator and denominator by : 
(sqrt(5)+sqrt(3)) 

gives: 

{[(sqrt(5)+sqrt(3))] ^ 2} / 2 

or 

4 + sqrt (15)

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chets

Sep 13, 2005

the reason i posted this question was to ask a second question. 

if you chose to multiply the numerator and denominator by sqrt(5)+sqrt(3) you get 4+sqrt(5)*sqrt(3) 

though, if you chose to multiply the numerator and denominator by sqrt(5)-sqrt(3) you get 1 / (4-sqrt(5)*sqrt(3)) 

though seemingly different, 

4+sqrt(5)*sqrt(3) = 1/(4-sqrt(5)*sqrt(3)) 

I am not sure whether there is a broad generalization i am missing. If anyone can shed light on this, that would be great!