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Arrange the following numbers in increasing order:

\(\begin{align*} A &= \frac{2^{1/2}}{4^{1/6}}\\ B &= \sqrt[12]{128}\vphantom{dfrac{2}{2}}\\ C &= \left( \frac{1}{8^{1/5}} \right)^2\\ D &= \sqrt{\frac{4^{-1}}{2^{-1} \cdot 8^{-1}}}\\ E &= \sqrt[3]{2^{1/2} \cdot 4^{-1/4}}.\vphantom{dfrac{2}{2}} \end{align*}\)

Enter the letters, separated by commas. For example, if you think that \(D < A < E < C < B\), then enter "D,A,E,C,B", without the quotation marks.

 Apr 4, 2020
 #1
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A  2^(1/2) / 4^(1/6)  =  2^(1/2) / ( 2^2)^(1/6)  = 2^(1/2) / 2^(1/3)  =  2^(1/2  - 1/3)  = 2^(1/6)

 

B    (128)^(1/28)  = [ 2^(7)]^(1/28)  = 2^(1/4)

 

C    (1 / 8^(1/5))^2  =  [ (8)^(-1/5)]^2  =  (2^3)^(-1/5)  = 2^(-3/5)

 

D     Note    4^(-1)  = 1/4       2^(-1)  = 1/2    8^(-1)  = 1/8

 

So  what  we have inside the radical is just this :

 

                1/4                        1/4

             _________   =    _______   =   (1/4) * (16/1)   =   4

              1/2  * 1/8                1/16  

 

And       the sqrt of this =   2

 

E     Inside  the radical  we have 

 

2^(1/2) * 4^(-1/4)  =

 

2^(1/2) * (2^2)^(-1/4)   =

 

2^(1/2) * 2^(-1/2)  =

 

2^(1/2 - 1/2) =

 

2^0  = 

 

1

 

And the cube root of this   is still   just 1

 

So  in order we have

 

2^(-3/5) ,  2^(1/6)  ,  2^(1/4) , 1 , 2

 

C , A , B , E , D

 Apr 4, 2020
 #2
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+1

The above answer was copy and pasted from here: https://web2.0calc.com/questions/a-good-math-question

 

(All except CPhill's signature coolcoolcool)

 

Guest, if you find the answer on another page, just provide a link to that page. Do not copy the answer as if it were your own. That is plagiarism and it is wrong.

 Apr 4, 2020
 #3
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Actually I checked and it said it wasnt right. Idk what went wrong. Both anwsers are wrong! help!

Guest Apr 6, 2020
 #4
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A =1.12246
B =1.498307
C =0.435275
D =2
E =1
C < E < A < B < D = C, E, A, B, D

 Apr 6, 2020
 #5
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0

Thanks so much! This one was correct! Thank you :)

Guest Apr 7, 2020

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