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Suppose that a, b, and c are real numbers such that a/b = sqrt(10)/sqrt(21) and b/c = sqrt(14)/sqrt(15). Find a/c. Completely simplify and rationalize the denominator.

 Jul 15, 2021
 #1
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 (a/b)*(b/c) = √10/√15. If we rationalize that, we get √150/15, which is 5√6/15, which is √6/3

 Jul 15, 2021
edited by Guest  Jul 15, 2021
 #2
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a/b =  sqrt (10)  / sqrt (21)

a  =    b sqrt (10)  /sqrt (21)

 

b/c =  sqrt (14)  / sqrt (15)

c/b  =  sqrt (15) / sqrt (14)

c = b sqrt (15)  / sqrt (14)

 

a / c   =      [ bsqrt (10) / sqrt (21)]  /  [ bsqrt (15)/sqrt (14) ] =

 

[sqrt (10) sqrt (14)]  /  [ sqrt (21) sqrt (15)]  =

 

sqrt (10) / sqrt (15)    *   sqrt (14) / sqrt (21)  =

 

sqrt  (10/15)  *  sqrt ( 14/21)   =

 

sqrt (2/3)  *  sqrt (2/3)   =

 

2/3

 

 

 

cool cool cool  

 Jul 15, 2021

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