How to simplify terms with usage of square root in maxima

Question

Let's say we have a term like 1/4 * x/sqrt(2) * x^2 / 2; in Maxima. As an output (without further modification) it gives x^3/2^(7/2). How can I force the output format to be like x^3/(8*sqrt(2)) with usage of square roots whenever possible?

Answer 1

(%i1) sq2: " "(sqrt(2))$
(%i2) matchdeclare(n, lambda([n], oddp(n) and n#1))$
(%i3) defrule(r_sq2, 2^(n/2), sq2*2^((n-1)/2))     $
(%i4) e: 1/4 * x/sqrt(2) * x^2 / 2;
                                       3
                                      x
(%o4)                                ----
                                      7/2
                                     2
(%i5) apply1(e, r_sq2);
                                             3
                                  (sqrt(2)) x
(%o5)                            -------------
                                      16

A rule can help to insert sqrt(2). In the example I use a "null" function to prevent simplification. You can also consider box and rembox functions or leave sq2 undefined.