When a non-zero number is squared or is raised to an EVEN integer power, it results in a positive number only. But, when the EVEN integer power is retrieved from the result, by taking the corresponding EVEN integer root of the result, the non-zero number reappears in its positive shape only, even if it was a negative originally. This ensures that the even roots (i.e. square root, 4th root, 6th root, etc) of a positive number are some positive numbers only; their negativity, if was there, never resurrects.

If x was the original non-zero number, then √x^2 = |x|, this |x| = x if x > 0, and/or |x| = -x if x < 0.

This untimely thread is in the fond memory of the following two threads

https://www.beatthegmat.com/mgmat-cat-qn ... 62756.html

https://www.beatthegmat.com/gmat-prep-sq ... 63401.html

Regards