Question 175653
the way one writes a problem makes a huge difference in math: the way I read you statement is 
:
{{{(1/2)/sqrt(3/2)}}} lets rewrite {{{sqrt(3/2)}}} to {{{sqrt(3)/sqrt(2)}}} and invert this and multiply by 1/2
:
{{{(1/2)(sqrt(2)/sqrt(3))}}}which equals{{{sqrt(2)/2sqrt(3)}}} now lets rationalize the denominator multiplying top and bottom by {{{sqrt(3)}}}
:
{{{sqrt(2)sqrt(3)/2 (3)cross(sqrt(3))cross(sqrt(3))}}} now combine terms
:
{{{highlight(sqrt(6)/6)}}}