Date: Mar 2, 2014 7:28 AM
Author: G. A. Edgar
Subject: Re: when is sqrt(a/b) not the same as sqrt(a)/sqrt(b) ?
> 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/