Question 113881
{{{sqrt(3x/2)}}} is what I think you mean.


Begin with the fact that {{{sqrt(a/b)=sqrt(a)/sqrt(b)}}} for all real a, and real b so long as {{{b<>0}}}.


So, {{{sqrt(3x/2)=sqrt(3x)/sqrt(2)}}}


However, simplest form requires that you have no radicals in the denominator, so you have to perform a process called 'rationalizing the denominator.'  To perform this process, you need to start with the ideas that {{{a * 1=a}}} for all real a and {{{a/a=1}}} for all real a, {{{a<>0}}}.  What we are going to do is multiply our expression by 1 in the form of {{{sqrt(2)/sqrt(2)}}}.


{{{(sqrt(3x)/sqrt(2))(sqrt(2)/sqrt(2))=(sqrt(3x)sqrt(2))/sqrt(2)sqrt(2)=sqrt(6x)/2}}}


And that is the simplest form for the given expression.


Hope that helps,
John