Is sqrt(4) Equal to +2 or -2 and Where Is the Error in My Calculation?

[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..

Thanks in advance

 

[luxiaolei]

2 = |sqrt(4)|

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

 

[Unit91Actual]

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..

Thanks in advance

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!

 

[luxiaolei]

Thanks Unit91Actual!

 

[willem2]

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!

$x^2 = 4$ 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

 

[Unit91Actual]

$x^2 = 4$ 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

Good point.