What does √a² make if a<0 : (A) +a, (B) -a, (C) ±a

√a² only returns the positive root, so
|a| would be the answer

|a| in terms of a:
If a < 0
then (multiply both sides by -1 and flip the sign)
-a > 0

So -a is |a|, meaning the answer is B

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It all depends on what  √a²  represents.

➊ If a < 0, then √ ̅a̅²̅ = │a│ = -a ⇒ (B)        ← ANSWER ... Note: If  a < 0, then  -a > 0

➋ If a < 0, then (√ ̅a̅̅  )² = a ⇒ (A)                ← ANSWER


Have a good one!
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Here is an easy way to find your answer, plug in any value that fits a<0 so -5 sqrt of (-5)^2 is the sqrt of 25 so the answer is C

B

(C) ±a