Answer :
To find the square roots of the number 441, we need to identify which values, when squared (multiplied by themselves), result in 441.
1. Calculate the Square Root of 441:
- The square root of 441 is 21. This is because 21 times 21 equals 441.
2. Identify Possible Square Roots:
- We have both positive and negative square roots to consider since both can be valid:
- 21 (because 21² = 441)
- -21 (because (-21)² = 441)
3. Check Each Option Given:
A. [tex]\(441^{1 / 2}\)[/tex]: This represents the square root of 441 which is 21.
B. 42: 42 times 42 equals 1764, not 441. So, it's not a square root of 441.
C. 21: As calculated, 21 is indeed a square root of 441.
D. [tex]\(-441^{1 / 2}\)[/tex]: This represents the negative square root of 441, which is -21.
E. 882: 882 times 882 is much larger than 441, so it cannot be a square root of 441.
F. -21: As previously determined, -21 is also a square root of 441.
4. Concluding Which Are Square Roots:
After evaluating each option, the correct square roots are:
- [tex]\(441^{1 / 2}\)[/tex] (Option A)
- 21 (Option C)
- [tex]\(-441^{1 / 2}\)[/tex] (Option D)
- -21 (Option F)
These options are the correct answers.
1. Calculate the Square Root of 441:
- The square root of 441 is 21. This is because 21 times 21 equals 441.
2. Identify Possible Square Roots:
- We have both positive and negative square roots to consider since both can be valid:
- 21 (because 21² = 441)
- -21 (because (-21)² = 441)
3. Check Each Option Given:
A. [tex]\(441^{1 / 2}\)[/tex]: This represents the square root of 441 which is 21.
B. 42: 42 times 42 equals 1764, not 441. So, it's not a square root of 441.
C. 21: As calculated, 21 is indeed a square root of 441.
D. [tex]\(-441^{1 / 2}\)[/tex]: This represents the negative square root of 441, which is -21.
E. 882: 882 times 882 is much larger than 441, so it cannot be a square root of 441.
F. -21: As previously determined, -21 is also a square root of 441.
4. Concluding Which Are Square Roots:
After evaluating each option, the correct square roots are:
- [tex]\(441^{1 / 2}\)[/tex] (Option A)
- 21 (Option C)
- [tex]\(-441^{1 / 2}\)[/tex] (Option D)
- -21 (Option F)
These options are the correct answers.
