Answer :
To find which of the given options are square roots of the number 121, we can follow these simple steps:
1. Understand the Concept: A square root of a number is a value that, when multiplied by itself, gives the original number. For example, if [tex]\( x^2 = 121 \)[/tex], then [tex]\( x \)[/tex] is a square root of 121.
2. Calculate the Square Root of 121: The number 121 is a perfect square. The positive square root of 121 is the number which, when squared, gives 121. We know that:
[tex]\[
11 \times 11 = 121
\][/tex]
Therefore, 11 is the positive square root.
3. Consider the Negative Square Root: Square roots can be both positive and negative since:
[tex]\[
(-11) \times (-11) = 121
\][/tex]
So, -11 is also a square root of 121.
4. Analyze the Options: Look at each option to determine which represent the square roots of 121:
- A. 48: Not a square root, as [tex]\( 48 \times 48 \neq 121 \)[/tex].
- B. [tex]\( 121^{1/2} \)[/tex]: This represents the positive square root of 121, which is 11. So, this is correct.
- C. 66: Not a square root, as [tex]\( 66 \times 66 \neq 121 \)[/tex].
- D. -11: As we determined, -11 is a square root since [tex]\((-11) \times (-11) = 121\)[/tex]. Thus, this is correct.
- E. [tex]\(-121^{1/2}\)[/tex]: This notation implies the negative of the positive square root, which is -11. Hence, this is also correct.
- F. 11: As we calculated, 11 is a square root, so this is correct.
5. Conclusion: The options that correctly identify the square roots of 121 are B, D, E, and F.
1. Understand the Concept: A square root of a number is a value that, when multiplied by itself, gives the original number. For example, if [tex]\( x^2 = 121 \)[/tex], then [tex]\( x \)[/tex] is a square root of 121.
2. Calculate the Square Root of 121: The number 121 is a perfect square. The positive square root of 121 is the number which, when squared, gives 121. We know that:
[tex]\[
11 \times 11 = 121
\][/tex]
Therefore, 11 is the positive square root.
3. Consider the Negative Square Root: Square roots can be both positive and negative since:
[tex]\[
(-11) \times (-11) = 121
\][/tex]
So, -11 is also a square root of 121.
4. Analyze the Options: Look at each option to determine which represent the square roots of 121:
- A. 48: Not a square root, as [tex]\( 48 \times 48 \neq 121 \)[/tex].
- B. [tex]\( 121^{1/2} \)[/tex]: This represents the positive square root of 121, which is 11. So, this is correct.
- C. 66: Not a square root, as [tex]\( 66 \times 66 \neq 121 \)[/tex].
- D. -11: As we determined, -11 is a square root since [tex]\((-11) \times (-11) = 121\)[/tex]. Thus, this is correct.
- E. [tex]\(-121^{1/2}\)[/tex]: This notation implies the negative of the positive square root, which is -11. Hence, this is also correct.
- F. 11: As we calculated, 11 is a square root, so this is correct.
5. Conclusion: The options that correctly identify the square roots of 121 are B, D, E, and F.
