Question 177826
{{{sqrt(2/3)(sqrt(27/2)-3/sqrt(2)))}}}
...((sqrt(27)/sqrt(2))-(3/sqrt(2)))
...(sqrt(27)-3)/sqrt(2)
...(sqrt(9*3)-3/sqrt(2)
...(3sqrt(3)-3)/sqrt(2)
(sqrt(2)/sqrt(3))(3sqrt(3)-3)/sqrt(2)
=(3sqrt(6)-3sqrt(2))/sqrt(6)
=sqrt(6)((3sqrt(6)-3sqrt(2))/6) Multiply top and bottom by sqrt(6) to eliminate the sqrt(6) in the denominator which is not allowed.
=(3sqrt(36)-3sqrt(12))/6
=(18-3sqrt(4*3))/6
=(18-6sqrt(3))/6
=3-sqrt(3)
.
Ed