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Re: How to get sqrt(Year^2)===Year?

• To: mathgroup at smc.vnet.net
• Subject: [mg75790] Re: How to get sqrt(Year^2)===Year?
• From: Bill Rowe <readnewsciv at sbcglobal.net>
• Date: Thu, 10 May 2007 05:24:11 -0400 (EDT)

On 5/9/07 at 4:33 AM, abbot at AugiaDives.hre (Hatto von Aquitanien)
wrote:

>If I have some expression which takes the square root of a square,
>it evaluates leaving the whole square root expression unchanged.

>Year == (Year^2)^(1/2)

>just returns what I entered when evaluated.

The reason this occurs is will not evaluate to True for all
possible values of the variable Year. For example, consider what
happens if Year = -1. The right hand side evaluates to 1 which
is clearly not what you started with.

However, you can use the Mathematica PowerExapnd to cause
(Year^2)^(1/2) to evaluate to Year, i.e.

In[1]:= Year == (Year^2)^(1/2) // PowerExpand

Out[1]= True

Just be aware this transformation will not be valid in general.
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