Answer :
To find the square roots of 576, we need to determine which of the given options are square roots of the number. Let's break it down:
1. Understanding Square Roots:
The square root of a number is any number that, when multiplied by itself, results in the original number. For 576, we need to find numbers [tex]\( x \)[/tex] such that [tex]\( x \times x = 576 \)[/tex].
2. List of Options:
We have the following options to check:
- A. 24
- B. -24
- C. [tex]\(-576^{1/2}\)[/tex]
- D. 48
- E. [tex]\(576^{1/2}\)[/tex]
- F. 12
3. Checking Each Option:
- A. 24:
[tex]\( 24 \times 24 = 576 \)[/tex]. So, 24 is a square root of 576.
- B. -24:
[tex]\((-24) \times (-24) = 576 \)[/tex]. Therefore, -24 is also a square root of 576 because a negative number multiplied by itself gives a positive result.
- C. [tex]\(-576^{1/2}\)[/tex]:
The expression represents [tex]\(-1\)[/tex] times the positive square root of 576, which results in -24. As determined earlier, -24 is a valid square root of 576.
- D. 48:
[tex]\( 48 \times 48 = 2304 \)[/tex], which is not equal to 576. So, 48 is not a square root of 576.
- E. [tex]\(576^{1/2}\)[/tex]:
This is another way to express the positive square root of 576, which is 24. We've already verified that 24 is a square root of 576.
- F. 12:
[tex]\( 12 \times 12 = 144 \)[/tex], which is not equal to 576. Thus, 12 is not a square root of 576.
4. Conclusion:
After evaluating all the options, the square roots of 576 are:
- A. 24
- B. -24
- C. [tex]\(-576^{1/2}\)[/tex] (which simplifies to -24)
- E. [tex]\(576^{1/2}\)[/tex] (which simplifies to 24)
These options match options A, B, C, and E, indicating these are indeed the square roots of 576.
1. Understanding Square Roots:
The square root of a number is any number that, when multiplied by itself, results in the original number. For 576, we need to find numbers [tex]\( x \)[/tex] such that [tex]\( x \times x = 576 \)[/tex].
2. List of Options:
We have the following options to check:
- A. 24
- B. -24
- C. [tex]\(-576^{1/2}\)[/tex]
- D. 48
- E. [tex]\(576^{1/2}\)[/tex]
- F. 12
3. Checking Each Option:
- A. 24:
[tex]\( 24 \times 24 = 576 \)[/tex]. So, 24 is a square root of 576.
- B. -24:
[tex]\((-24) \times (-24) = 576 \)[/tex]. Therefore, -24 is also a square root of 576 because a negative number multiplied by itself gives a positive result.
- C. [tex]\(-576^{1/2}\)[/tex]:
The expression represents [tex]\(-1\)[/tex] times the positive square root of 576, which results in -24. As determined earlier, -24 is a valid square root of 576.
- D. 48:
[tex]\( 48 \times 48 = 2304 \)[/tex], which is not equal to 576. So, 48 is not a square root of 576.
- E. [tex]\(576^{1/2}\)[/tex]:
This is another way to express the positive square root of 576, which is 24. We've already verified that 24 is a square root of 576.
- F. 12:
[tex]\( 12 \times 12 = 144 \)[/tex], which is not equal to 576. Thus, 12 is not a square root of 576.
4. Conclusion:
After evaluating all the options, the square roots of 576 are:
- A. 24
- B. -24
- C. [tex]\(-576^{1/2}\)[/tex] (which simplifies to -24)
- E. [tex]\(576^{1/2}\)[/tex] (which simplifies to 24)
These options match options A, B, C, and E, indicating these are indeed the square roots of 576.
