Answer :
To determine which options are square roots of 484, we start by understanding the concept of a square root. A square root of a number is a value that, when multiplied by itself, gives the original number.
Let's check each option:
1. Option A: -22
- When -22 is multiplied by itself:
[tex]\[
(-22) \times (-22) = 484
\][/tex]
- Therefore, -22 is a square root of 484.
2. Option B: 22
- When 22 is multiplied by itself:
[tex]\[
22 \times 22 = 484
\][/tex]
- So, 22 is also a square root of 484.
3. Option C: 44
- When 44 is multiplied by itself:
[tex]\[
44 \times 44 = 1936
\][/tex]
- Since 1936 is not equal to 484, 44 is not a square root of 484.
4. Option D: [tex]\(484^{1/2}\)[/tex]
- The expression [tex]\(484^{1/2}\)[/tex] represents the positive square root of 484.
- [tex]\[
484^{1/2} = 22
\][/tex]
- This is indeed a square root of 484.
5. Option E: 242
- When 242 is multiplied by itself:
[tex]\[
242 \times 242 = 58564
\][/tex]
- Since 58564 is not equal to 484, 242 is not a square root of 484.
6. Option F: [tex]\(-484^{1/2}\)[/tex]
- The expression [tex]\(-484^{1/2}\)[/tex] represents the negative square root of 484.
- [tex]\[
-484^{1/2} = -22
\][/tex]
- This is also a square root of 484.
Conclusion:
The options that are square roots of 484 are:
- A. -22
- B. 22
- D. [tex]\(484^{1/2}\)[/tex]
- F. [tex]\(-484^{1/2}\)[/tex]
Let's check each option:
1. Option A: -22
- When -22 is multiplied by itself:
[tex]\[
(-22) \times (-22) = 484
\][/tex]
- Therefore, -22 is a square root of 484.
2. Option B: 22
- When 22 is multiplied by itself:
[tex]\[
22 \times 22 = 484
\][/tex]
- So, 22 is also a square root of 484.
3. Option C: 44
- When 44 is multiplied by itself:
[tex]\[
44 \times 44 = 1936
\][/tex]
- Since 1936 is not equal to 484, 44 is not a square root of 484.
4. Option D: [tex]\(484^{1/2}\)[/tex]
- The expression [tex]\(484^{1/2}\)[/tex] represents the positive square root of 484.
- [tex]\[
484^{1/2} = 22
\][/tex]
- This is indeed a square root of 484.
5. Option E: 242
- When 242 is multiplied by itself:
[tex]\[
242 \times 242 = 58564
\][/tex]
- Since 58564 is not equal to 484, 242 is not a square root of 484.
6. Option F: [tex]\(-484^{1/2}\)[/tex]
- The expression [tex]\(-484^{1/2}\)[/tex] represents the negative square root of 484.
- [tex]\[
-484^{1/2} = -22
\][/tex]
- This is also a square root of 484.
Conclusion:
The options that are square roots of 484 are:
- A. -22
- B. 22
- D. [tex]\(484^{1/2}\)[/tex]
- F. [tex]\(-484^{1/2}\)[/tex]
