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

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The discussion centers on the confusion surrounding the square root of 4, specifically whether it equals +2 or -2. The key error identified is in the misuse of the property that allows the separation of square roots, which only holds true when both factors are non-negative. While both +2 and -2 are solutions to the equation x^2 = 4, the notation sqrt(4) specifically refers to the principal square root, which is +2. The misunderstanding arises from incorrectly applying the square root properties in the calculations. Ultimately, sqrt(4) is defined as +2, not -2.
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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
 
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Feldoh said:
2 = |sqrt(4)|

Thanks!,how silly am I...gosh...
 
luxiaolei said:
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!
 
Thanks Unit91Actual!
 
Unit91Actual said:
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
 
willem2 said:
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.
 

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