Answer :
To solve the problem of identifying which options are square roots of 49, let's consider the definition of a square root. A number that, when multiplied by itself, gives the original number is a square root. Here, the number is 49, so we're looking for numbers which multiply by themselves to result in 49.
Let's go through the options:
- A. -7: When we multiply -7 by itself (-7 -7), we get 49. So, -7 is indeed a square root of 49.
- B. 7: When we multiply 7 by itself (7 7), we also get 49. Therefore, 7 is a square root of 49.
- C. 8: When we multiply 8 by itself (8 8), we get 64, not 49. So, 8 is not a square root of 49.
- D. [tex]\(-49^{1/2}\)[/tex]: The expression [tex]\(-49^{1/2}\)[/tex] typically represents the negative of the square root of 49. The square root of 49 is 7, so this option simplifies to -7. Since we know -7 is a square root of 49, this option is correct.
- E. 28: When we multiply 28 by itself (28 28), we get a much larger number, specifically 784, not 49. Thus, 28 is not a square root of 49.
- F. [tex]\(49^{1/2}\)[/tex]: This expression is the positive square root of 49, which calculates to 7. Since 7 is a square root of 49, this option is correct.
Based on this analysis, the correct options that are square roots of 49 are A (-7), B (7), D ([tex]\(-49^{1/2}\)[/tex]), and F ([tex]\(49^{1/2}\)[/tex]).
Let's go through the options:
- A. -7: When we multiply -7 by itself (-7 -7), we get 49. So, -7 is indeed a square root of 49.
- B. 7: When we multiply 7 by itself (7 7), we also get 49. Therefore, 7 is a square root of 49.
- C. 8: When we multiply 8 by itself (8 8), we get 64, not 49. So, 8 is not a square root of 49.
- D. [tex]\(-49^{1/2}\)[/tex]: The expression [tex]\(-49^{1/2}\)[/tex] typically represents the negative of the square root of 49. The square root of 49 is 7, so this option simplifies to -7. Since we know -7 is a square root of 49, this option is correct.
- E. 28: When we multiply 28 by itself (28 28), we get a much larger number, specifically 784, not 49. Thus, 28 is not a square root of 49.
- F. [tex]\(49^{1/2}\)[/tex]: This expression is the positive square root of 49, which calculates to 7. Since 7 is a square root of 49, this option is correct.
Based on this analysis, the correct options that are square roots of 49 are A (-7), B (7), D ([tex]\(-49^{1/2}\)[/tex]), and F ([tex]\(49^{1/2}\)[/tex]).
