The discussion revolves around the mathematical manipulation of square roots involving negative numbers, specifically the expression \((-6)^{1/2} \times (-7)^{1/2} = (42)^{1/2}\). Participants are exploring the validity of the steps taken in the calculation and the properties of square roots.
Some participants have pointed out potential errors in the original poster's reasoning, particularly regarding the assumption that the property \(x^z y^z = (xy)^z\) holds for negative values. Others have suggested that the right-hand side of the equation should remain unchanged during manipulation.
There is an implicit assumption that the properties of square roots apply universally, which is being challenged in the context of negative numbers. The discussion is also constrained by the need to adhere to homework guidelines that may limit the exploration of complex numbers.
((-6)^ 1/2 ) ( (-7)^1/2) = (42)^1/2frozen7 said:((-6)^ 1/2 ) ( (-7)^1/2) = (42)^1/2
((-6)^ 1/2 ) ( (-7)^1/2) = (6^ 1/2 ) ( 7^1/2) ( i ^2)
= -(42)^1/2
Can anyone tell me where I did wrong?