Answer:
False
Step-by-step explanation:
Step 1: Determine if the expression [tex]\(\sqrt{a^2}\)[/tex] always equals [tex]\(±a\)[/tex] for any real or non-real number [tex]\(a\)[/tex]. = False
Step 2: Explain why [tex]\(\sqrt{a^2} = ±a\)[/tex] is not always true for any real or non-real number [tex]\(a\)[/tex]. =
The expression [tex]\(\sqrt{a^2}\)[/tex] is defined as the non-negative square root of [tex]\(\sqrt{a^2}\)[/tex], which means it always yields the absolute value of [tex]\(a\)[/tex], denoted as [tex]\(|a|\)[/tex]. Therefore, [tex]\(\sqrt{a^2} = |a|\)[/tex], not [tex]\(±a\)[/tex]. For non-negative [tex]\(a\)[/tex], [tex]\(\sqrt{a^2} = a\)[/tex], and for negative [tex]\(a\)[/tex], [tex]\(\sqrt{a^2} = -a\)[/tex]. Thus, the expression does not include the negative value when [tex]\(a\)[/tex] is positive, contradicting the claim that [tex]\(\sqrt{a^2} = ±a\)[/tex].
(I... tried my best for this one. I'm not 100% sure if it's right, but I tried... TvT)
