Question 848999
You are trying to show  {{{35=3*(8.5)+(root(3,a)+169)}}} according to what you wrote.


First, isolate the root(3,a).
{{{35=3(8.5)+root(3,a)+169}}}
{{{root(3,a)=35-3(8.5)-169}}}, the parentheses not having any effect.
{{{root(3,a)=-159.5}}}
This is the same as {{{-root(3,a)=159.5}}}; and the result would be irrational.  


There are methods to do this by hand; or you could do it in in a more simple manner using or starting from known cubes of whole numbers.  You could go a bit fancier and use logarithms.  No matter how to go through, the result will be an approximation.


{{{5^3=125}}}; {{{6^3=216}}};  you would or could test values between 5 and 6, being something near to 5.5.
(You would find that {{{5.50^3=166.375}}}, and {{{5.4^3=157.464}}}; you might then either try linear interpolation, or look for another cubic multiplication between 5.4 and 5.5.)