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

289

A. 17
B. [tex]$289^{1 / 2}$[/tex]
C. [tex]$-289^{1 / 2}$[/tex]
D. -17
E. 88
F. 150

To determine which options are square roots of 289, follow these steps:

1. Understanding Square Roots: A square root of a number is a value that, when multiplied by itself, gives the original number. Each positive number has two square roots: one positive and one negative.

2. Identify the Square Roots of 289:
- The positive square root of 289 is 17 because [tex]$17 \times 17 = 289$[/tex].
- The negative square root of 289 is -17 because [tex]$-17 \times -17 = 289$[/tex].

3. Evaluate Each Option:
- Option A: 17
→ 17 is the positive square root of 289.

- Option B: [tex]$289^{1/2}$[/tex]
→ [tex]$289^{1/2}$[/tex] represents the positive square root of 289, which is also 17.

- Option C: [tex]$-289^{1/2}$[/tex]
→ [tex]$-289^{1/2}$[/tex] represents the negative square root of 289, which is -17.

- Option D: -17
→ -17 is the negative square root of 289.

- Option E: 88
→ 88 is neither a positive nor a negative square root of 289, since [tex]$88 \times 88 \neq 289$[/tex].

- Option F: 150
→ 150 is neither a positive nor a negative square root of 289, since [tex]$150 \times 150 \neq 289$[/tex].

4. Conclusion: The square roots of 289 listed in the options are:
- A: 17
- B: [tex]$289^{1/2}$[/tex] (which equals 17)
- C: [tex]$-289^{1/2}$[/tex] (which equals -17)
- D: -17

These options correctly represent the square roots of 289.