Re: Canceling square roots with Simplify

*To*: mathgroup at smc.vnet.net*Subject*: [mg18257] Re: Canceling square roots with Simplify*From*: Adam Strzebonski <adams at wolfram.com>*Date*: Thu, 24 Jun 1999 14:24:40 -0400*Organization*: Wolfram Research, Inc.*References*: <7kpage$49n@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

efarr wrote: > > Hello, > > Try typing in the following in a new session of Mathematica (I'm currently > running ver 3.0 under WinNT). > > Simplify[ Sqrt[b^2]*Sqrt[1/b^2] ] > > It seems like the b's should cancel, and I should get 1. Why don't I? Is > there any workaround? > > Thanks very much > > Everett G. Farr The expression needs not to be equal to 1 for complex values of b: In[1]:= Sqrt[b^2]*Sqrt[1/b^2] /. b->I Out[1]= -1 To get the simplification anyway you can use PowerExpand, which uses the transformation (a^b)^c -> a^(b*c). In[1]:= PowerExpand[Sqrt[b^2]*Sqrt[1/b^2]] Out[1]= 1 However, you need to keep in mind that the transformation is not correct in general, so the results obtained using PowerExpand may not be correct for all values of parameters. In Mathematica 4 you can get the simplification by telling Simplify that b is real. In[2]:= Simplify[Sqrt[b^2]*Sqrt[1/b^2], Element[b, Reals]] Out[2]= 1 Best Regards, Adam Strzebonski Wolfram Research