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Re: How to Multiply Sqrt[a] with Sqrt[b]

  • To: mathgroup at smc.vnet.net
  • Subject: [mg38182] Re: [mg38134] How to Multiply Sqrt[a] with Sqrt[b]
  • From: Vladimir Bondarenko <vvb at mail.strace.net>
  • Date: Wed, 4 Dec 2002 03:26:12 -0500 (EST)
  • In-reply-to: <200212030934.EAA14825@smc.vnet.net>
  • References: <200212030934.EAA14825@smc.vnet.net>
  • Reply-to: Vladimir Bondarenko <vvb at mail.strace.net>
  • Sender: owner-wri-mathgroup at wolfram.com

"Gernot Pfanner" <pfannerg at kfunigraz.ac.at> wrote on Tuesday, December 03, 2002, 5:34:51 AM :

GP> Does somebody know an algorithm to simplify the product  Sqrt[a]*Sqrt[b] ?

Apply Simplify or FullSimplify with Assumptions.

Generally speaking, over the complex plane, Sqrt[a]*Sqrt[b] cannot be
simplified further, and Mathematica "knows" it.

  In[1] := FullSimplify[Sqrt[x]Sqrt[y], x \[Element] Complexes]

  Out[1] = Sqrt[x]*Sqrt[y]

The same holds for the real plane.

  In[2] := FullSimplify[Sqrt[x] Sqrt[y], x \[Element] Reals]

  Out[2] = Sqrt[x]*Sqrt[y]

Sometimes, if your work over the real plane, things might look simpler.

  In[3] := Simplify[Sqrt[x] Sqrt[y], x > 0 && y > 0]

  Out[3] = Sqrt[x*y]

  In[4] := Simplify[Sqrt[x] Sqrt[y], x < 0 && y < 0]

  Out[4] = -Sqrt[x*y]

and so on.


Best wishes,

Vladimir Bondarenko
Mathematical and Production Director
Symbolic Testing Group

        http://www.CAS-testing.org/  GEMM Project             (95% ready)

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