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RE: Canceling square roots with Simplify


Earlier I replied to a message where Everett Farr asked why
Simplify[ Sqrt[b^2]*Sqrt[1/b^2] ]
doesn't simplify to 1.

As already noted by Adam Strzebonski the expression above isn't equal to 1
for all values of (b).  One counter example is when (b=I).

For basically the same reason the rule I thought is missing from the 
Simplify routine isn't true in general and shouldn't be included.


The rule that isn't true in general is:
----------------
MyRules= {
 ((zb_^(-1*z1_))^(z2_)):>((zb^z1)^(-z2)),
 ((zb_^p_?Negative)^z2_):>(zb^(-p))^(-z2)  };
----------------

As Adam Strzebonski noted one can use PowerExpand get the expected result.
Also using version 4 one can use Simplify/FullSimplify and indicate certain
variables are part of a specific domain to get the expected result.

Regards,
Ted Ersek
 


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