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Topic: when is sqrt(a/b) not the same as sqrt(a)/sqrt(b) ?
Replies: 8   Last Post: Mar 5, 2014 3:34 PM

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G. A. Edgar

Posts: 2,499
Registered: 12/8/04
Re: when is sqrt(a/b) not the same as sqrt(a)/sqrt(b) ?
Posted: Mar 2, 2014 7:28 AM
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> I have always thought that sqrt(a/b) and sqrt(a)/sqrt(b) are
> exactly the same
>


Certainly sqrt(a/b) and sqrt(a)/sqrt(b) are both square roots of a/b.
But a complex number has two square roots. It could happen (as Axel
explains), that the "principal branch" choice for sqrt results in
opposite choices for these two. If a,b are both positive, this does
not happen, and you get the same square root.

Similar things can happen with other powers, with logarithgms, inverse
trig functions, and so on. Unless you choose the arguments nicely
enough.

--
G. A. Edgar http://www.math.ohio-state.edu/~edgar/



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