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Answer :
To determine which numbers are square roots of 576, we can calculate the square root of 576 and identify both the positive and negative values since a number has both a positive and a negative square root.
1. Calculate the positive square root of 576:
- The positive square root of 576 is 24 because [tex]\(24 \times 24 = 576\)[/tex].
2. Consider both positive and negative roots:
- The number 24 is a positive square root of 576.
- Consequently, -24 is the negative square root of 576, as [tex]\((-24) \times (-24) = 576\)[/tex].
3. Examine each option:
- A. 12: 12 is not a square root of 576 because [tex]\(12 \times 12 = 144\)[/tex], which is not equal to 576.
- B. [tex]\(-576^{1/2}\)[/tex]: The notation [tex]\(-576^{1/2}\)[/tex] implies taking the negative of the square root of 576. This equals -24, since 576's square root is 24, and we use the negative sign.
- C. 24: This is correct because 24 is the positive square root of 576.
- D. -24: This is correct because -24 is the negative square root of 576.
- E. 48: 48 is not a square root of 576 because [tex]\(48 \times 48 = 2304\)[/tex], which is not equal to 576.
- F. [tex]\(576^{1/2}\)[/tex]: This represents the positive square root, which is 24.
Based on this analysis, the correct choices are:
- B. [tex]\(-576^{1/2}\)[/tex]
- C. 24
- D. -24
- F. [tex]\(576^{1/2}\)[/tex]
1. Calculate the positive square root of 576:
- The positive square root of 576 is 24 because [tex]\(24 \times 24 = 576\)[/tex].
2. Consider both positive and negative roots:
- The number 24 is a positive square root of 576.
- Consequently, -24 is the negative square root of 576, as [tex]\((-24) \times (-24) = 576\)[/tex].
3. Examine each option:
- A. 12: 12 is not a square root of 576 because [tex]\(12 \times 12 = 144\)[/tex], which is not equal to 576.
- B. [tex]\(-576^{1/2}\)[/tex]: The notation [tex]\(-576^{1/2}\)[/tex] implies taking the negative of the square root of 576. This equals -24, since 576's square root is 24, and we use the negative sign.
- C. 24: This is correct because 24 is the positive square root of 576.
- D. -24: This is correct because -24 is the negative square root of 576.
- E. 48: 48 is not a square root of 576 because [tex]\(48 \times 48 = 2304\)[/tex], which is not equal to 576.
- F. [tex]\(576^{1/2}\)[/tex]: This represents the positive square root, which is 24.
Based on this analysis, the correct choices are:
- B. [tex]\(-576^{1/2}\)[/tex]
- C. 24
- D. -24
- F. [tex]\(576^{1/2}\)[/tex]
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