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Re: Convincing Mathematica that Sqrt[a+b]Sqrt[a-b]==Sqrt[a^2+b^2]

• To: mathgroup at smc.vnet.net
• Subject: [mg63284] Re: Convincing Mathematica that Sqrt[a+b]Sqrt[a-b]==Sqrt[a^2+b^2]
• From: Bhuvanesh <lalu_bhatt at yahoo.com>
• Date: Thu, 22 Dec 2005 00:04:49 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

> Is there a way to convince Mathematica to multiply
> Sqrt[a+b]Sqrt[a-b] to produce Sqrt[a^2+b^2]?

Simplify with assumptions can do it:

In[1]:= Simplify[Sqrt[a + b]*Sqrt[a - b], a >= b] //InputForm

Out[1]//InputForm= Sqrt[a^2 - b^2]

Of course, that equality isn't true in general.

Bhuvanesh,
Wolfram Research.