Answer :
To determine which options are the square roots of [tex]\(121\)[/tex], let's evaluate each choice:
1. Understanding Square Roots:
- The square root of a number [tex]\(x\)[/tex] is a number [tex]\(y\)[/tex] such that [tex]\(y \times y = x\)[/tex].
- For the number [tex]\(121\)[/tex], two numbers can satisfy this: the positive square root and the negative one, since [tex]\((\pm y)^2 = y^2\)[/tex].
2. Calculating the Square Roots of 121:
- The positive square root of [tex]\(121\)[/tex] is [tex]\(11\)[/tex] because [tex]\(11 \times 11 = 121\)[/tex].
- The negative square root is [tex]\(-11\)[/tex] because [tex]\((-11) \times (-11) = 121\)[/tex].
3. Checking each option:
- A. [tex]\(121^{1 / 2}\)[/tex]: This is another way of representing the square root of [tex]\(121\)[/tex]. The value is [tex]\(11\)[/tex], a valid square root.
- B. [tex]\(11\)[/tex]: As calculated, [tex]\(11\)[/tex] is indeed a square root of [tex]\(121\)[/tex].
- C. [tex]\(48\)[/tex]: [tex]\(48 \times 48 = 2304\)[/tex], which is not equal to [tex]\(121\)[/tex]. So, [tex]\(48\)[/tex] is not a square root.
- D. [tex]\(66\)[/tex]: [tex]\(66 \times 66 = 4356\)[/tex], which is not equal to [tex]\(121\)[/tex]. Thus, [tex]\(66\)[/tex] is not a square root.
- E. [tex]\(-11\)[/tex]: As previously determined, [tex]\(-11\)[/tex] is the negative square root of [tex]\(121\)[/tex].
- F. [tex]\(-121^{1 / 2}\)[/tex]: This represents the negative square root of [tex]\(121\)[/tex] as well, which is [tex]\(-11\)[/tex].
4. Conclusion:
- The correct options that represent square roots of [tex]\(121\)[/tex] are A, B, E, and F.
These options correctly indicate the values that, when squared, result in [tex]\(121\)[/tex].
1. Understanding Square Roots:
- The square root of a number [tex]\(x\)[/tex] is a number [tex]\(y\)[/tex] such that [tex]\(y \times y = x\)[/tex].
- For the number [tex]\(121\)[/tex], two numbers can satisfy this: the positive square root and the negative one, since [tex]\((\pm y)^2 = y^2\)[/tex].
2. Calculating the Square Roots of 121:
- The positive square root of [tex]\(121\)[/tex] is [tex]\(11\)[/tex] because [tex]\(11 \times 11 = 121\)[/tex].
- The negative square root is [tex]\(-11\)[/tex] because [tex]\((-11) \times (-11) = 121\)[/tex].
3. Checking each option:
- A. [tex]\(121^{1 / 2}\)[/tex]: This is another way of representing the square root of [tex]\(121\)[/tex]. The value is [tex]\(11\)[/tex], a valid square root.
- B. [tex]\(11\)[/tex]: As calculated, [tex]\(11\)[/tex] is indeed a square root of [tex]\(121\)[/tex].
- C. [tex]\(48\)[/tex]: [tex]\(48 \times 48 = 2304\)[/tex], which is not equal to [tex]\(121\)[/tex]. So, [tex]\(48\)[/tex] is not a square root.
- D. [tex]\(66\)[/tex]: [tex]\(66 \times 66 = 4356\)[/tex], which is not equal to [tex]\(121\)[/tex]. Thus, [tex]\(66\)[/tex] is not a square root.
- E. [tex]\(-11\)[/tex]: As previously determined, [tex]\(-11\)[/tex] is the negative square root of [tex]\(121\)[/tex].
- F. [tex]\(-121^{1 / 2}\)[/tex]: This represents the negative square root of [tex]\(121\)[/tex] as well, which is [tex]\(-11\)[/tex].
4. Conclusion:
- The correct options that represent square roots of [tex]\(121\)[/tex] are A, B, E, and F.
These options correctly indicate the values that, when squared, result in [tex]\(121\)[/tex].
