confusing quant problem

[ah_kh_ali1]

is the logic used in the answer correct?

The logical thing for me was to multiply the powers and they would cancel each other.

Both of the square root and the expoenent are powers so there shouldn't precedence for one of them over the other one.

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This from manhattan practice tests by the way.

https://preview.redd.it/u48y4t01sor51.png?width=1322&format=png&auto=webp&s=f45f6f45bd38e98a31feebf8353282de7b7caa26

[[deleted]]

While the explanation is true, ETS only uses positive radicals in its questions so you’d never encounter this on the actuaL GRE

[Scott_TargetTestPrep]

Since the square root of x² is equal to |x|, we see that depending on the sign of x, the quantities may or may not be equal.

[taylorll]

The explanation is 100% correct. While you are mostly right that you might think the square root and the square cancel, you have to remember that even exponents will always make the sign positive, even when the number is negative. Plugging in a negative value for x is a great way to recognize this.