Understanding the Complexities of Square Roots in Equations

[madness]

I have come up with a simple "paradox" (obviously I am doing something wrong). Sorry I can't use latex:

(-1)/1=1/(-1), take square root of both sides, so sqrt((-1)/1)=sqrt(1/(-1))
use sqrt(a/b)=srt(a)/sqrt(b) *, so i/1=1/i, implies i squared =1.

I think the problem is the part marked *, but I'm not sure in what circumstances this is valid. Can anybody help?

 

[yyat]

The problem is that every number except 0 actually has two square roots with opposite sign. You can arbitrarily choose one for each number, but then the formula sqrt(a/b)=srt(a)/sqrt(b) is not always true (as you demonstrated).

See also http://en.wikipedia.org/wiki/Square_root#Notes"

 

[madness]

Ok that helps a lot. The example on wikipedia was pretty much exactly the one I posted. Thanks.