What about applying PowerExpand?
In[2]:= Sqrt[PowerExpand[(Sqrt[2] - 1)^2]] Out[2]= -1 + Sqrt[2] In[3]:= Sqrt[PowerExpand[(Sqrt[3] - Sqrt[2])^2]] Out[3]= -Sqrt[2] + Sqrt[3]
Dear Bill,
This is an amazing package! What license have you published it under? May I use it and derivative work in my open source projects?
Vladimir: Sorry to have only now seen your query. License? Corey wrote this years ago while of highschool age, and appears to lack further interest in it. He has moved on from mathematics (http://www.blurb.com/b/2172660-minskys-trinskys-3rd-edition) to software engineering. I believe his chief concern with this package is not to be contacted when someone finds a bug! --Bill