Answer :
To determine which of the given options are square roots of 49, let's go through each one:
1. Square Roots of 49:
- The square roots of a number are the values that, when multiplied by themselves, give the original number. For the number 49, the square roots are 7 and -7, because [tex]\(7 \times 7 = 49\)[/tex] and [tex]\((-7) \times (-7) = 49\)[/tex].
2. Checking Each Option:
- A. [tex]\(49^{1/2}\)[/tex]:
- [tex]\(49^{1/2}\)[/tex] refers to the positive square root of 49, which is 7. So, this is correct.
- B. [tex]\(-49^{1/2}\)[/tex]:
- [tex]\(-49^{1/2}\)[/tex] refers to the negative square root of 49, which is -7. So, this is correct.
- C. 8:
- 8 is not a square root of 49 because [tex]\(8 \times 8 = 64\)[/tex], which is not 49.
- D. 7:
- As reasoned earlier, 7 is a square root of 49 because [tex]\(7 \times 7 = 49\)[/tex].
- E. -7:
- Similarly, -7 is a square root of 49 because [tex]\((-7) \times (-7) = 49\)[/tex].
- F. 28:
- 28 is not a square root of 49 because [tex]\(28 \times 28 = 784\)[/tex], which is not 49.
3. Conclusion:
The values that are square roots of 49 from the given options are:
- A. [tex]\(49^{1/2}\)[/tex]
- B. [tex]\(-49^{1/2}\)[/tex]
- D. 7
- E. -7
These are the correct answers, as they represent either the positive or negative square roots of 49.
1. Square Roots of 49:
- The square roots of a number are the values that, when multiplied by themselves, give the original number. For the number 49, the square roots are 7 and -7, because [tex]\(7 \times 7 = 49\)[/tex] and [tex]\((-7) \times (-7) = 49\)[/tex].
2. Checking Each Option:
- A. [tex]\(49^{1/2}\)[/tex]:
- [tex]\(49^{1/2}\)[/tex] refers to the positive square root of 49, which is 7. So, this is correct.
- B. [tex]\(-49^{1/2}\)[/tex]:
- [tex]\(-49^{1/2}\)[/tex] refers to the negative square root of 49, which is -7. So, this is correct.
- C. 8:
- 8 is not a square root of 49 because [tex]\(8 \times 8 = 64\)[/tex], which is not 49.
- D. 7:
- As reasoned earlier, 7 is a square root of 49 because [tex]\(7 \times 7 = 49\)[/tex].
- E. -7:
- Similarly, -7 is a square root of 49 because [tex]\((-7) \times (-7) = 49\)[/tex].
- F. 28:
- 28 is not a square root of 49 because [tex]\(28 \times 28 = 784\)[/tex], which is not 49.
3. Conclusion:
The values that are square roots of 49 from the given options are:
- A. [tex]\(49^{1/2}\)[/tex]
- B. [tex]\(-49^{1/2}\)[/tex]
- D. 7
- E. -7
These are the correct answers, as they represent either the positive or negative square roots of 49.
