# Simple question,Help

1. Feb 16, 2010

### luxiaolei

2 = sqrt(4) = sqrt(-1*-1*4) = sqrt(-1)*sqrt(-1)*sqrt(4) = -1*sqrt(4) = -2 ?????

Where am I wrong? sqrt(4) = +2 or -2 in the last step? but see sqrt(4)=-1*sqrt(4), still wrong..

2. Feb 16, 2010

### luxiaolei

Thanks!,how silly am I.....gosh...

3. Feb 16, 2010

### Unit91Actual

The real problem here lies in the first step, not the last. 2 is a solution to √4, but is not the solution. Your conundrum has simply re-stated that -2 is also a solution to √4. This string of equations does not prove that 2 = -2 (obviously), only that the solution to √4 is non-unique. Good luck!

4. Feb 16, 2010

### luxiaolei

Thanks Unit91Actual!

5. Feb 16, 2010

### willem2

$x^2 = 4$ has two solutions, but sqrt(4) means the positive solution of this equations.
The other one is -sqrt(4).
2 = sqrt(-1 * -1 * 4) is OK, but the next step is not since sqrt(A*B) = sqrt(A) * sqrt(B) is only valid if A and B are >= 0

6. Feb 16, 2010

Good point.