The discussion revolves around the interpretation of the square root of 4, specifically whether sqrt(4) should be considered as +2 or -2, and where errors may lie in the calculations presented by participants. The scope includes mathematical reasoning and clarification of concepts related to square roots.
Participants generally agree that sqrt(4) is defined as +2, but there is a recognition that -2 is also a solution to the equation x^2 = 4. The discussion reflects multiple views on the manipulation of square roots and the conditions under which certain mathematical properties apply, indicating that the topic remains somewhat contested.
The discussion reveals limitations in understanding the properties of square roots, particularly regarding the conditions under which certain mathematical operations are valid. There is also a lack of consensus on the interpretation of the square root notation in this context.
Feldoh said:2 = |sqrt(4)|
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
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!
willem2 said:[itex]x^2 = 4[/itex] 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