Is √(a-1)² positive or negative (a≠1)

Positive because for any number n:

(n*n) and (-n)*(-n) is always positive hence (a-1)^2 is always positives.

Then the square root sign as written always refers to the positive square root of a number.

The way you have written it does not make the order of operations clear. Technically the square root operation should be taken first as it appears first (left to right), but this may be how it appeared in the original problem.

If the question requires you to take the square root of (a-1) and then square it afterwards then the result will always be positive as squaring any (real) number always gives you a positive.

If the question requires you to square (a-1) and then take the square root then there will be both a positive and a negative answer. The square of (a-1) will always be positive for real numbers and then the square root of this will either be sqrt((a-1)^2) or -sqrt((a-1)^2). Both answers are equally correct (mathematically speaking)

(a-1)^2 never can be negative.... So sq. Root of (a-1)^2= always positive.
Coz: consider (a-1)= -ve
therefore, -ve^2= - x - =+= positive
N.B. Remember anything's[real no.] square is always positive.

a≠1 => a-1≠0 => (a-1)²>0

√c≥0 by def

Hence
√(a-1)² is positive

√(a-1)² = a-1 if a>1 and 1-a if a<1
since by convention √ refers to the positive root, as others
have pointed out.

positive (it will always be the square root of a positive number even if 'a' is negative).