Question 895695
What?  Which?


{{{1/root(3,3)+1}}}
Multiply only the first rational expression by {{{(root(3,3)root(3,3))/(root(3,3)root(3,3))}}}


{{{1/(root(3,3)+1)}}}
A little trickier.
A very good piece of guidance is shown, here:
<a href="http://www.purplemath.com/modules/radicals7.htm">http://www.purplemath.com/modules/radicals7.htm</a>


OR still, you you mean,
{{{1/root(3,3+1)}}}
?



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If your expression is the first one or the last one, then rationalizing the denominator is very simple.


IF you have THIS ONE,  {{{highlight_green(1/(root(3,3)+1))}}}, then this is how and what to know:


Polynomial division of {{{a^3+b^3}}} by {{{a+b}}} will give the quotient, {{{a^2-ab+b^2}}}.


Starting with {{{1/(root(3,3)+1)}}} and using {{{root(3,3)=a}}} and {{{1=b}}}, rationalize the denominator
through multiplication of the expression by 1.


This 1 uses {{{(root(3,3))^2-root(3,3)+1}}} in numerator and denominator.


{{{(1/(root(3,3)+1))(((root(3,3))^2-root(3,3)+1)/((root(3,3))^2-root(3,3)+1))}}}


{{{((root(3,3))^2-root(3,3)+1)/((root(3,3))^3+1^3)}}}


{{{((root(3,3))^2-root(3,3)+1)/(3+1)}}}


{{{highlight(((root(3,3))^2-root(3,3)+1)/4)}}}