Answer :
To find the square roots of the number 49, we need to determine which options correctly represent the square roots.
1. Understanding Square Roots:
- The square root of a number is a value that, when multiplied by itself, gives the original number.
- For the number 49, its square roots are numbers that can be squared to get 49.
2. Considering the Options:
- A. 8: Squaring 8 gives [tex]\(8 \times 8 = 64\)[/tex]. This is not equal to 49, so 8 is not a square root.
- B. [tex]\(49^{1/2}\)[/tex]: This expression represents the operation of taking the square root of 49. The square root of 49 is indeed 7, so this is a correct square root.
- C. -7: Squaring -7 gives [tex]\((-7) \times (-7) = 49\)[/tex]. This is another valid square root since squaring a negative number results in a positive value.
- D. 7: Squaring 7 gives [tex]\(7 \times 7 = 49\)[/tex], making 7 a correct square root.
- E. 28: Squaring 28 gives [tex]\(28 \times 28 = 784\)[/tex]. This is not equal to 49, so 28 is not a square root.
- F. [tex]\(-49^{1/2}\)[/tex]: This expression means the negative of the square root of 49, which is [tex]\(-7\)[/tex]. As we saw, -7 is indeed a valid square root of 49.
3. Conclusion:
- The correct options that are square roots of 49 are B ([tex]\(49^{1/2}\)[/tex]), C (-7), D (7), and F ([tex]\(-49^{1/2}\)[/tex]).
Therefore, the square roots of 49 from the given choices are B, C, D, and F.
1. Understanding Square Roots:
- The square root of a number is a value that, when multiplied by itself, gives the original number.
- For the number 49, its square roots are numbers that can be squared to get 49.
2. Considering the Options:
- A. 8: Squaring 8 gives [tex]\(8 \times 8 = 64\)[/tex]. This is not equal to 49, so 8 is not a square root.
- B. [tex]\(49^{1/2}\)[/tex]: This expression represents the operation of taking the square root of 49. The square root of 49 is indeed 7, so this is a correct square root.
- C. -7: Squaring -7 gives [tex]\((-7) \times (-7) = 49\)[/tex]. This is another valid square root since squaring a negative number results in a positive value.
- D. 7: Squaring 7 gives [tex]\(7 \times 7 = 49\)[/tex], making 7 a correct square root.
- E. 28: Squaring 28 gives [tex]\(28 \times 28 = 784\)[/tex]. This is not equal to 49, so 28 is not a square root.
- F. [tex]\(-49^{1/2}\)[/tex]: This expression means the negative of the square root of 49, which is [tex]\(-7\)[/tex]. As we saw, -7 is indeed a valid square root of 49.
3. Conclusion:
- The correct options that are square roots of 49 are B ([tex]\(49^{1/2}\)[/tex]), C (-7), D (7), and F ([tex]\(-49^{1/2}\)[/tex]).
Therefore, the square roots of 49 from the given choices are B, C, D, and F.
