Question 48636
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Please help. These problems look so easy but I just can't seem to get the right answer.
First Problem:
1/√3 + 4/√27 - 2/√12


Second Problem:
2 cubed root of 27x + 2 cubed root 64x
I came up with 2 answers:
14 cubed root of x -OR- 2 cubed root of 91x
Which one is correct??
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        In the post by @consc198, first solution is irrelevant,  while second solution is incorrect.


        For right solutions,  see what follows.



<pre>
        F i r s t   p r o b l e m


It does not say what to do and what is required, but according to common sense, 
they want you to simplify and to reduce to simple canonic final form.


  {{{1/sqrt(3)}}} + {{{4/sqrt(27)}}} - {{{2/sqrt(12)}}} = 

= {{{1/sqrt(3)}}} + {{{4/(3*sqrt(3))}}} - {{{2/(2*sqrt(3))}}} = 

= {{{(1/sqrt(3))*(1 + (4/3) - 1)}}} = {{{4/(3*sqrt(3))}}} = {{{(4*sqrt(3))/(3*3)}}} = {{{(4/9)*sqrt(3)}}}.    <U>ANSWER</U>




        S e c o n d   p r o b l e m


  {{{2*root(3,27x)}}} + {{{2*root(3,64x)}}} = 


       Notice that  27 = 3^3,  while  64 = 4^3.

       So, we continue the chain of equalities


= {{{2*3*root(3,x) + 2*4*root(3,x)}}} = {{{6*root(3,x)}}} + {{{8*root(3,x)}}} = {{{14*root(3,x)}}}.    <U>the correct ANSWER</U>
</pre>

Solved.


As this person, @consc198, solves simple standard Math problems, he deserves to be excluded 
from everywhere of an educational community, because he is not able to teach in a right way.