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It makes a difference. In the first expression we do not know if (a+2) is positive or negative. In the second expression, since a+2 is inside of a square root, we know that a+2 cannot be negative.
Both of these expressions look like they would simplify to a+2. But square roots are supposed to be positive (or zero). With the first expression, since we do not if a+2 is positive we must use absolute value to ensure that we have a positive (or zero) result.
With the second expression, since we know that a+2 cannot be negative, we do not need absolute value:
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