High School

Which of the following are square roots of the number 576? Check all that apply.

A. 48
B. 12
C. [tex]-576^{1/2}[/tex]
D. 24
E. -24
F. [tex]576^{1/2}[/tex]

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.