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Manipulating square roots

• To: mathgroup at smc.vnet.net
• Subject: [mg112341] Manipulating square roots
• From: alan <alansbarnett at verizon.net>
• Date: Fri, 10 Sep 2010 04:48:07 -0400 (EDT)

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?