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In Mathematica, Simplify[1/Sqrt[a] == Sqrt[1/a]] gives Sqrt[1/a] == 1/Sqrt[a]. I don't really see why this doesn't give a true output when, FullSimplify gives the desired result.

This probably is a very dumb question, but I just don't see it.

Tzar
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Wille Bell
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2 Answers2

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Because if a<0 then sqrt can have complex output values.

For example 

sqrt(1/-1)=i

while 

1/sqrt(-1)=-i

See wiki.

T.Lucas
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0

You can specify assumptions to Simplify.

Simplify[1/Sqrt[a] == Sqrt[1/a], a >= 0]
(* True *)
Rohit Namjoshi
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