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Which of the following are square roots of the number below? Check all that apply.

121

A. -11
B. 11
C. [tex]$121^{1/2}$[/tex]
D. [tex]$-121^{1/2}$[/tex]
E. 48
F. 66

Answer :

To find the square roots of 121, we need to identify the numbers that, when multiplied by themselves, give 121. The solutions can be both positive and negative because multiplying two negative numbers results in a positive number.

Here is a step-by-step explanation:

1. Identify the positive square root:
- The number 11, when multiplied by itself (11 × 11), equals 121. Therefore, 11 is a square root of 121.

2. Identify the negative square root:
- Similarly, the number -11, when multiplied by itself (-11 × -11), also equals 121. Hence, -11 is another square root of 121.

3. Verification using expressions:
- The expression [tex]\(121^{1/2}\)[/tex] represents the positive square root of 121, which is 11.
- The expression [tex]\(-121^{1/2}\)[/tex] represents the negative square root of 121, which is -11.

4. Review the options:
- Option A corresponds to -11, which is correct.
- Option B corresponds to 11, which is also correct.
- Option C ([tex]\(121^{1/2}\)[/tex]) evaluates to 11, making it correct.
- Option D ([tex]\(-121^{1/2}\)[/tex]) evaluates to -11, making it correct.
- Options E (48) and F (66) do not result in 121 when squared.

So, the correct answers are:
- A. -11
- B. 11
- C. [tex]\(121^{1/2}\)[/tex]
- D. [tex]\(-121^{1/2}\)[/tex]

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