# Is there a function or option to collect factors under one radical sign?

One of the things that frustrates me most about Mathematica's symbolic manipulations is the fact that output is often presented quite differently than most humans would write it. This is especially egregious when square roots are involved. For example, Mathematica will output this

when I think most humans (or at least physicists) would consider this to be "simpler":

or, alternatively,

My question is: Is there any simplification function, option, or other trick for coercing Mathematica into formatting an output thusly? I have so far not had any success finding one, and I've explored various simplification formulas as well as trying to apply assumptions about the variables (real, positive, etc.) -- though maybe I just haven't stumbled on the right one.

• Providing copyable code will increase the likelihood and speed of answers. Apr 15, 2015 at 17:24
• I get nervous whenever factions start to collect under one radical. Apr 15, 2015 at 20:04
• @Mr.Wizard: Noted. Thanks. Apr 16, 2015 at 2:24

Your transformation is not generally true; if you provide FullSimplify with your assumptions you get a better result:
expr = (Sqrt[2] Sqrt[Ea - g L m])/Sqrt[m];

Sqrt[-2 g L + (2 Ea)/m]

• @ibeatty You could Factor the expression under the radical but then Mathematica would automatically convert it to Sqrt[2] Sqrt[-((-Ea + g L m)/m)]. I am not aware of any general and successful strategy to make Mathematica format expressions in "human" form, though there are tools and formats that are at least useful, e.g. TraditionalForm, HornerForm, etc. This has been asked before; I'll try to find a reference. Apr 15, 2015 at 18:34