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Answer :
To determine which options are square roots of 576, let's go through each choice:
A. 48:
48 is not a square root of 576 because [tex]\( 48 \times 48 \neq 576 \)[/tex].
B. 12:
12 is not a square root of 576 because [tex]\( 12 \times 12 \neq 576 \)[/tex].
C. [tex]\(-576^{1/2}\)[/tex]:
This represents the negative square root of 576. [tex]\(-576^{1/2}\)[/tex] is a valid square root for 576, as it represents the negative version of the principal square root.
D. 24:
24 is indeed a square root of 576 because [tex]\( 24 \times 24 = 576 \)[/tex].
E. -24:
-24 is also a square root of 576 because [tex]\((-24) \times (-24) = 576\)[/tex]. Remember, both positive and negative versions of a number can be square roots.
F. [tex]\(576^{1/2}\)[/tex]:
This represents the positive principal square root of 576, which is a valid square root.
So, the square roots of 576 include options C, D, E, and F.
A. 48:
48 is not a square root of 576 because [tex]\( 48 \times 48 \neq 576 \)[/tex].
B. 12:
12 is not a square root of 576 because [tex]\( 12 \times 12 \neq 576 \)[/tex].
C. [tex]\(-576^{1/2}\)[/tex]:
This represents the negative square root of 576. [tex]\(-576^{1/2}\)[/tex] is a valid square root for 576, as it represents the negative version of the principal square root.
D. 24:
24 is indeed a square root of 576 because [tex]\( 24 \times 24 = 576 \)[/tex].
E. -24:
-24 is also a square root of 576 because [tex]\((-24) \times (-24) = 576\)[/tex]. Remember, both positive and negative versions of a number can be square roots.
F. [tex]\(576^{1/2}\)[/tex]:
This represents the positive principal square root of 576, which is a valid square root.
So, the square roots of 576 include options C, D, E, and F.
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