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Suppose that a, b, and c are real numbers such that $\frac{a}{b} = \frac{\sqrt{10}}{\sqrt{21}}$ and $\frac{b}{c} = \frac{\sqrt{135}}{\sqrt{42}}$. Find $\frac{a}{c}$. Completely simplify and rationalize the denominator.

 Apr 11, 2022
 #1
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+1

a/b  * b/c    =   a / c  =   sqrt (10)  / sqrt (42)  *   sqrt (135) / sqrt (42)  =

 

sqrt (2) sqrt (5)                 sqrt (5 ) sqrt (27)

_____________   *         _______________   =

sqrt (2) sqrt (21)              sqrt (2) sqrt (21)

 

 

5 sqrt (27)

_____________  =

21 sqrt (2) 

 

 

5 sqrt (27) sqrt (2)

_______________   =

21 sqrt (2) sqrt (2)

 

 

5 sqrt (54)

_________   = 

   42

 

5 sqrt (9) sqrt (6)

_____________     =

       42

 

15 sqrt (6)

________    =

     42

 

5 sqrt (6)

________

    14

 

 

cool cool cool

 Apr 11, 2022

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