Clarification:
I need a listable function that can find and replace every occurrence of Power[z1,1/2]*Power[z2,1/2] in a data set of several hundred thousand equations with Power[z1 z2,1/2] without effecting anything else in the data set.
How does one take an expression like Sqrt[a+b]Sqrt[a-b] and get Mathematica to return Sqrt[a^2-b^2], or said differently, what is the opposite of PowerExpand (neither Simplify nor FullSimplify is the answer)?
I've tried some basic pattern matching with no luck, that boils down to the fact I don't know how to pattern match the sequence of Power[z1,1/2]Power[z2,1/2].
All suggestions are appreciated.
BTW: because of what "b" is in my problem Sqrt[a^2-b^2] = c, which then goes on to cancel with other terms so this issue creates a major bottleneck in simplifying an very complex problem.