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Re: Manipulating square roots

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  • Subject: [mg112357] Re: Manipulating square roots
  • From: Peter Breitfeld <phbrf at>
  • Date: Fri, 10 Sep 2010 05:54:47 -0400 (EDT)
  • References: <i6crc2$s62$>

alan wrote:

> How can I get mathematica to bring a factor inside a square root?  For
> instance
> a Sqrt(1-(b/a)^2)  -> Sqrt(a^2-b^2)  (if a is real and a > 0).
> Also, how do I get Mathematica to perform the operation in reverse?

To get a under the root is easy:

new=Simplify[a Sqrt[1-(b/a)^2], a>0]

For the reverse, you might use a rule:

new/.Sqrt[a_^2-b_^2]:>a Sqrt[1-(b/a)^2]

This will work in this simple case, but fail if e.g. the root is in the
denominator, because then the FullForm no longer matches the pattern

Peter Breitfeld, Bad Saulgau, Germany --

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