According to ETS we are not supposed to consider the negative root of a radical right. In the above solution from manhattan 5lb(#6 algebra) they have considered the negative root to solve, i wanted to know if that’s valid? thank u in advance.

Hi feel the manhattan considers negative roots, but as far Greg had mentioned ETS wont suppose to consider.

Not sure if this is previous ETS question, or just manhattans question, where they thought ETS may consider negative roots

No, also according to ETS the result would be here the same since here they are not considering the negative root of something but a negative number squared which, also according to ETS, results in a positive number. Again: ETS would not have you calculate the square root of -16, but it would have you calculate -2^2.

if the problem contains a variable squared, or some other algebra that leads to a variable squared, and you yourself take a square root as part of the act of solving, then you always have to consider all possible solutions, both the positive square roots and the negative square roots.

Source:https://magoosh.com/gre/positive-and-negative-square-roots-on-the-gre/