Rick,
For the audience understand better of 'The SEM equals SD / sqrt(N). '.
I think could write it as

STD(MEAN)=sqrt( VAR(MEAN) )
= sqrt( VAR( (x1+x2+...xn)/n ) )
= sqrt( VAR(x1+x2+...xn)/n^2 ) )
= sqrt( n*VAR(x)/n^2 ) )
= sqrt( VAR(x)/n ) )
= sqrt( VAR(x) ) / sqrt(N)
= SD / sqrt(N)