Question 973570
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Use this factoring pattern:<br>
{{{a^3-b^3=(a-b)(a^2+ab+b^2)}}}<br>
With {{{a=root(3,2)}}} and {{{b=1}}}, this becomes<br>
{{{2-1=(root(3,2)-1)(root(3,4)+root(3,2)+1)}}}<br>
Your expression is<br>
{{{1/root(3,2)}}}<br>
To rationalize the denominator, you need to multiply numerator and denominator by<br>
{{{(root(3,4)+root(3,2)+1)}}}<br>
Then<br>
{{{(1/root(3,2))((root(3,4)+root(3,2)+1)/(root(3,4)+root(3,2)+1))=(root(3,4)+root(3,2)+1)/(2-1)=(root(3,4)+root(3,2)+1)}}}<br>
... which is the answer you say you are supposed to get<br>