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Answer :
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.
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.
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