Question 973570
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Hi,

Well I've run into a problem that I can't really do.

The question is to rationalise 1/(cube root 2 - 1). The answer is cube root 2 + cube root 4 + 1. I know
how to rationalise 1/cube root 2 but I'm not sure how to do this one. What I got is:

1/cube root 2-1=1/cube root 2-1 * (cube root 2^2 + 1)/(cube root 2^2 + 1)

And I've so on and so forth, but I didn't get the right answer. I got cube root 4 + 1.

Thanks
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If this is {{{1/(root (3, 2) - 1)}}}, then your 1st answer, "cube root 2 + cube root 4 + 1," is WRONG, but the 2nd, "cube
root 4 + 1," is CORRECT!! See BELOW!!

{{{1/(root (3, 2) - 1)}}} = {{{1/(- 1 + root (3, 2))}}} 
{{{1/(- 1 + root (3, 2))}}} * {{{(- 1 - root (3, 4))/(- 1 - root (3, 4))}}} ---- Rationalizing denominator by MULTIPLYING numerator and denominator by {{{- 1 - root (3, 2^2)}}} = {{{- 1 - root (3, 4)}}} 
{{{(1(- 1 - root (3, 4)))/((- 1 + root (3, 2))(- 1 - root (3, 4)))}}} = {{{(- 1 - root (3, 4))/((- 1)^2 - (root (3, 2))(root (3, 4)))}}} = {{{(- 1 - root (3, 4))/((- 1)^2 - root (3, 2*4))}}} = {{{(- 1 - root (3, 4))/((- 1)^2 - root (3, 8))}}} = {{{(- 1 - root (3, 4))/(1 - 2)}}} = {{{(- 1 - root (3, 4))/(- 1)}}} = {{{highlight(1 + root (3, 4)))}}}</font></font></font></b></pre>