       Re: Manipulating square roots

• To: mathgroup at smc.vnet.net
• Subject: [mg112357] Re: Manipulating square roots
• From: Peter Breitfeld <phbrf at t-online.de>
• Date: Fri, 10 Sep 2010 05:54:47 -0400 (EDT)
• References: <i6crc2\$s62\$1@smc.vnet.net>

```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
Sqrt[a_^2-b_^2]

--
_________________________________________________________________
Peter Breitfeld, Bad Saulgau, Germany -- http://www.pBreitfeld.de

```

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