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

121

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

Answer :

To find the square roots of a number, we look for all numbers [tex]\( r \)[/tex] such that

[tex]$$
r^2 = 121.
$$[/tex]

Since

[tex]$$
\sqrt{121} = 11,
$$[/tex]

the equation can be written as

[tex]$$
r^2 = 11^2,
$$[/tex]

which implies that

[tex]$$
r = \pm 11.
$$[/tex]

Thus, the two square roots of [tex]\( 121 \)[/tex] are [tex]\( 11 \)[/tex] and [tex]\( -11 \)[/tex].

Now, let’s identify which of the provided options represent either [tex]\( 11 \)[/tex] or [tex]\( -11 \)[/tex]:

1. Option A: [tex]\( -121^{1/2} \)[/tex]
This means [tex]\( -\sqrt{121} \)[/tex], which is [tex]\( -11 \)[/tex].

2. Option B: [tex]\( -11 \)[/tex]
This is clearly [tex]\( -11 \)[/tex].

3. Option C: [tex]\( 66 \)[/tex]
[tex]\( 66 \)[/tex] is not equal to either [tex]\( 11 \)[/tex] or [tex]\( -11 \)[/tex].

4. Option D: [tex]\( 121^{1/2} \)[/tex]
This is [tex]\( \sqrt{121} \)[/tex], which is [tex]\( 11 \)[/tex].

5. Option E: [tex]\( 48 \)[/tex]
[tex]\( 48 \)[/tex] is not equal to [tex]\( 11 \)[/tex] or [tex]\( -11 \)[/tex].

6. Option F: [tex]\( 11 \)[/tex]
This is [tex]\( 11 \)[/tex].

Thus, the square roots of [tex]\( 121 \)[/tex] are represented by Options A, B, D, and F.

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