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    $\begingroup$ Could you post Mathematica syntax ? $\endgroup$ Commented May 2, 2013 at 12:19
  • $\begingroup$ FullSimplify[ Sqrt[a] Sqrt[b]/(Sqrt[c] Sqrt[d]), {a > 0, b > 0, c > 0, d > 0}] $\endgroup$ Commented May 2, 2013 at 13:14
  • $\begingroup$ chuy, the aim is to have such a function for arbitrary expressions under the square roots. $\endgroup$ Commented May 2, 2013 at 13:20
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    $\begingroup$ Consider Sqrt[-2] Sqrt[-2] != Sqrt[4] and Sqrt[-3] Sqrt[-1/3] != 1. $\endgroup$ Commented May 2, 2013 at 13:21
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    $\begingroup$ works well for Sqrt[a] Sqrt[b] c, but fails with Sqrt[a]/Sqrt[b] $\endgroup$ Commented May 9, 2013 at 8:15