High School

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

[tex]484[/tex]

A. 22
B. 242
C. 44
D. [tex]-484^{1/2}[/tex]
E. [tex]484^{1/2}[/tex]
F. -22

Answer :

To find the square roots of the number 484, we'll need to identify both its positive and negative square roots. Remember that a square root of a number is a value which, when multiplied by itself, gives the original number.

Let's break this down step-by-step:

1. Calculate the Positive Square Root:
- The positive square root of 484 is 22 because [tex]\( 22 \times 22 = 484 \)[/tex].

2. Calculate the Negative Square Root:
- The negative square root is simply the negative of the positive square root, which is -22. This is because [tex]\( (-22) \times (-22) = 484 \)[/tex].

Now, let's match these results with the given options:

- A. 22: This is correct because 22 is the positive square root of 484.
- B. 242: This is not correct, because 242 is not a square root of 484.
- C. 44: This is not correct, because 44 is not a square root of 484.
- D. [tex]\(-484^{1 / 2}\)[/tex]: This expression represents the negative square root of 484, which is -22. So this is correct.
- E. [tex]\(484^{1 / 2}\)[/tex]: This expression represents the positive square root of 484, which is 22.
- F. -22: This is correct as -22 is the negative square root of 484.

Therefore, the correct answers are A, D, E, and F.

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