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Answer :
To determine which of the options are square roots of 121, let's first recall what a square root is. The square roots of a number are the values that, when multiplied by themselves, give the original number.
For the number 121, there are two primary square roots:
1. A positive square root: 11
2. A negative square root: -11
Now, let's evaluate each option to see if it matches one of these square roots:
- Option A: 66
66 is not a square root of 121 because 66 × 66 equals 4356, which is much larger than 121.
- Option B: [tex]\(-121^{1/2}\)[/tex]
This represents the negative square root of 121, which is indeed -11. Therefore, Option B is a square root.
- Option C: 48
48 is not a square root of 121 because 48 × 48 equals 2304, which is greater than 121.
- Option D: 11
11 is the positive square root of 121. Thus, Option D is a correct choice.
- Option E: -11
As mentioned earlier, -11 is the negative square root of 121, so this option is correct.
- Option F: [tex]\(121^{1/2}\)[/tex]
This represents the positive square root, which is 11. Therefore, Option F is correct as well.
In summary, the correct options that are square roots of 121 are B, D, E, and F.
For the number 121, there are two primary square roots:
1. A positive square root: 11
2. A negative square root: -11
Now, let's evaluate each option to see if it matches one of these square roots:
- Option A: 66
66 is not a square root of 121 because 66 × 66 equals 4356, which is much larger than 121.
- Option B: [tex]\(-121^{1/2}\)[/tex]
This represents the negative square root of 121, which is indeed -11. Therefore, Option B is a square root.
- Option C: 48
48 is not a square root of 121 because 48 × 48 equals 2304, which is greater than 121.
- Option D: 11
11 is the positive square root of 121. Thus, Option D is a correct choice.
- Option E: -11
As mentioned earlier, -11 is the negative square root of 121, so this option is correct.
- Option F: [tex]\(121^{1/2}\)[/tex]
This represents the positive square root, which is 11. Therefore, Option F is correct as well.
In summary, the correct options that are square roots of 121 are B, D, E, and F.
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