# What rule am I breaking here?

1. Mar 8, 2009

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?

2. Mar 8, 2009

### 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).