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Answer :
To find which of the options are square roots of 484, we need to identify both the positive and negative square roots of this number.
First, let's determine the principal square root of 484:
1. Calculate the Positive Square Root:
- The positive square root of 484 is 22, because [tex]\(22 \times 22 = 484\)[/tex].
2. Consider the Negative Square Root:
- The negative square root would be -22, because [tex]\(-22 \times -22 = 484\)[/tex].
With this understanding, let's examine each provided option to see if it matches the square roots we found:
A. -22
- This matches our negative square root, so it is correct.
B. 44
- This is not correct, because 44 is not a square root of 484. [tex]\(44 \times 44 = 1936\)[/tex].
C. 22
- This matches our positive square root, so it is correct.
D. [tex]\(484^{1/2}\)[/tex]
- This expression represents the positive square root of 484, which is 22, so it is correct.
E. [tex]\(-484^{1/2}\)[/tex]
- This expression represents the negative square root of 484, which is -22, so it is correct.
F. 242
- This is not correct, because 242 is not a square root of 484.
Therefore, the answers that are square roots of 484 are: A (-22), C (22), D ([tex]\(484^{1/2}\)[/tex]), and E ([tex]\(-484^{1/2}\)[/tex]).
First, let's determine the principal square root of 484:
1. Calculate the Positive Square Root:
- The positive square root of 484 is 22, because [tex]\(22 \times 22 = 484\)[/tex].
2. Consider the Negative Square Root:
- The negative square root would be -22, because [tex]\(-22 \times -22 = 484\)[/tex].
With this understanding, let's examine each provided option to see if it matches the square roots we found:
A. -22
- This matches our negative square root, so it is correct.
B. 44
- This is not correct, because 44 is not a square root of 484. [tex]\(44 \times 44 = 1936\)[/tex].
C. 22
- This matches our positive square root, so it is correct.
D. [tex]\(484^{1/2}\)[/tex]
- This expression represents the positive square root of 484, which is 22, so it is correct.
E. [tex]\(-484^{1/2}\)[/tex]
- This expression represents the negative square root of 484, which is -22, so it is correct.
F. 242
- This is not correct, because 242 is not a square root of 484.
Therefore, the answers that are square roots of 484 are: A (-22), C (22), D ([tex]\(484^{1/2}\)[/tex]), and E ([tex]\(-484^{1/2}\)[/tex]).
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