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Re: Manipulating square roots
Posted:
Sep 11, 2010 5:45 AM


The Presentations package has a routine FactorOut that is useful here. The trick is to pull a "factor" out of an expression and then protect the result so that Mathematica won't simplify it back.
FactorOut[factor, quotientfunction : Indentity, factorfunction : Identity][expr] will pull factor out of expression and write the result as factorfunction[factor] quotentfunction[Expand[expr/factor]].Factor would not even have to be in expr. The functions, if not Identity, would most commonly be HoldForm.
Here we go back and forth between the two forms.
Needs["Presentations`Master`"]
expr = Sqrt[a^2  b^2];
step1 = MapAt[FactorOut[a^2, HoldForm], expr, 1]
step2 = Simplify[step1, a > 0] // ReleaseHold
Giving...
Sqrt[a^2 (1b^2/a^2)]
a Sqrt[1  b^2/a^2]
step3 = MapAt[FactorOut[1/a^2, HoldForm], step2, {2, 1}]
step4 = Simplify[step3, a > 0] // ReleaseHold
Giving...
a Sqrt[(a^2b^2)/a^2]
Sqrt[a^2  b^2]
This has the advantage of doing it by calculation, but a simple rule as you wrote might be simpler. It depends on the context in which you are doing the transformation.
David Park djmpark@comcast.net http://home.comcast.net/~djmpark/
From: alan [mailto:alansbarnett@verizon.net]
How can I get mathematica to bring a factor inside a square root? For instance a Sqrt(1(b/a)^2) > Sqrt(a^2b^2) (if a is real and a > 0). Also, how do I get Mathematica to perform the operation in reverse?



