I would think it was a simple mistake if she hadn't cotinued to argue it. in the 10 minutes spent discussing it, she never once said anything about maybe mistakenly putting the wrong question in, despite my repeated attempts to convince her that it was not possible for both to be true (X^3=6, and 6 X^2=36)

the way cubed root of 8 came out was because she was factoring....36? I think. either way you do it it comes out as that cannot be right.