College

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

[tex]484[/tex]

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

Answer :

To find which options are square roots of 484, we need to understand what square roots are. A square root of a number is a value that, when squared, gives back the original number.

For the number 484:

1. Calculate the square root of 484.
- The number 22 when squared (22 × 22) equals 484. So, 22 is a square root of 484.
- The number -22 when squared (-22 × -22) also equals 484 because the product of two negative numbers is positive. So, -22 is also a square root of 484.

Now, let's check each option:

- Option A: [tex]\(484^{1/2}\)[/tex]
- [tex]\(484^{1/2}\)[/tex] means the square root of 484, which is 22. This option is correct.

- Option B: 242
- 242 is not a square root of 484 because 242 × 242 is much larger than 484. This option is not correct.

- Option C: 22
- As calculated, 22 is a square root of 484. This option is correct.

- Option D: 44
- 44 is not a square root of 484 because 44 × 44 is 1936, which is more than 484. This option is not correct.

- Option E: -22
- As calculated, -22 is a square root of 484. This option is correct.

- Option F: [tex]\(-484^{1/2}\)[/tex]
- [tex]\(-484^{1/2}\)[/tex] is the negative of the square root of 484, which is -22. This option is correct.

Therefore, the correct square roots of 484 from the given options are A, C, E, and F.

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