ETS notation for square root

GRE GRE Quant Problem Solving
1

I have a question about ETS notation.

I understand that sqrt64=8 (the principal square root), not ±8.

However, if a GRE Quantitative Comparison question gives only:

x2=1x^2 = 1x2=1

with no other information about xxx, and asks us to compare:

Quantity A: xxx

Quantity B: 111

Should we consider both x=1x = 1x=1 and x=−1x = -1x=−1, making the answer D, or does ETS ever expect us to take only the positive value?

More generally, is it always safe on the GRE to assume that a variable can be either positive or negative unless the question explicitly states otherwise?

2

When you’re solving x^2 = 1, you’re not making an exception and claiming \sqrt{1} = \pm 1. \sqrt{1} is still 1.