Two month plan - Week 1 - Day 3 - Exponents and roots 2

Hi!
So, in the Two month plan, Week 1, Day 3, and in the Exponents and Roots 2 video, Greg sir had explained a question around the 57:00 timestamp which I’ve posted below.

How I solved it: For the first equation, I squared the values on both sides of the equation to get rid of the root, and derived the value of ‘x’ to be 8. For the second equation, I took square roots on both sides of the equation and found the value of ‘y’ to be (+)8.

This method was followed by a student from the video as well, to which sir explained that this is not the right method and is used as a trick question by ETS. (Note: He had mentioned the answer to be option D, but I’m unable to view the options for this question in the recorded lecture, so I’m not sure what the options were.)

My question is, should we consider the negative root as an answer while square rooting a perfect square? While I understand that it is a valid answer generally in Mathematics, I remember Greg sir mentioning during the previous recorded classes that ETS doesn’t consider the negative root unless there is a negative sign before the radical (square root symbol). Please help me out with this. Thanks in advance!

It’s a QC (quantitative comparison) question. See Study Plans FAQ | Greg Mat Helpdesk

No. \sqrt{x} is always non-negative.

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Hi! Thank you so much for the link provided. It puts a lot of questions into perspective.

I want to clarify a little regarding the square root of x. If for example, we take the equation ‘y^2 = 4’, we’ll get the roots to be +2 and -2 (during Mathematics generally) when we take the square root on both sides right?

So, in GRE exam, should I consider -2 as a root or not? If not, could you please help me understand what sir is mentioning in the video? Thank you!

That yes. However, \sqrt{4} = 2. To see why, try plotting the graph of \sqrt{x}.

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Okay will do! Thank you so much for your time!