Answer :
To determine which options are square roots of 49, let's go through each step carefully:
1. Understand Square Roots:
- A square root of a number is a value that, when multiplied by itself, gives the original number. For the number 49, we are looking for numbers that multiply by themselves to equal 49.
2. Calculate the Square Roots of 49:
- The positive square root of 49 is 7, because [tex]\(7 \times 7 = 49\)[/tex].
- There is also a negative square root. The negative square root of 49 is -7, because [tex]\(-7 \times -7 = 49\)[/tex].
3. Check Each Option:
- A. 28: This is not a square root of 49 since [tex]\(28 \times 28\)[/tex] is much larger than 49.
- B. 8: Similarly, [tex]\(8 \times 8 = 64\)[/tex], which is not 49.
- C. [tex]\(49^{1/2}\)[/tex]: This represents the positive square root of 49, which is 7.
- D. 7: As calculated, 7 is indeed a positive square root of 49.
- E. [tex]\(-49^{1/2}\)[/tex]: This notation signifies the negative square root of 49, which corresponds to -7.
- F. -7: As discussed, -7 is the negative square root of 49.
4. Identify the Correct Answers:
- From the options given, both 7 and -7 are square roots of 49.
Therefore, the correct options that are square roots of 49 are D (7) and F (-7).
1. Understand Square Roots:
- A square root of a number is a value that, when multiplied by itself, gives the original number. For the number 49, we are looking for numbers that multiply by themselves to equal 49.
2. Calculate the Square Roots of 49:
- The positive square root of 49 is 7, because [tex]\(7 \times 7 = 49\)[/tex].
- There is also a negative square root. The negative square root of 49 is -7, because [tex]\(-7 \times -7 = 49\)[/tex].
3. Check Each Option:
- A. 28: This is not a square root of 49 since [tex]\(28 \times 28\)[/tex] is much larger than 49.
- B. 8: Similarly, [tex]\(8 \times 8 = 64\)[/tex], which is not 49.
- C. [tex]\(49^{1/2}\)[/tex]: This represents the positive square root of 49, which is 7.
- D. 7: As calculated, 7 is indeed a positive square root of 49.
- E. [tex]\(-49^{1/2}\)[/tex]: This notation signifies the negative square root of 49, which corresponds to -7.
- F. -7: As discussed, -7 is the negative square root of 49.
4. Identify the Correct Answers:
- From the options given, both 7 and -7 are square roots of 49.
Therefore, the correct options that are square roots of 49 are D (7) and F (-7).
