Answer :
To determine which of the given options are square roots of 49, we'll first understand what it means to be a square root.
A number is a square root of another number if, when it is multiplied by itself, it equals the original number. In this case, we're looking for numbers that, when squared, equal 49.
Let's analyze each option:
A. 28:
- If we square 28 (28 × 28), the result is 784, not 49. Therefore, 28 is not a square root of 49.
B. [tex]$-49^{1 / 2}$[/tex]:
- The expression [tex]$49^{1 / 2}$[/tex] indicates taking the square root of 49. In this context, however, the use of `-49` inside a square root suggests a complex or undefined value, so this is not a valid interpretation for our purpose.
C. [tex]$49^{1 / 2}$[/tex]:
- [tex]$49^{1 / 2}$[/tex] means the positive square root of 49. So, it is indeed a square root of 49.
D. 7:
- 7 × 7 = 49, so 7 is a square root of 49.
E. 8:
- 8 × 8 = 64, which does not equal 49. Thus, 8 is not a square root of 49.
F. -7:
- (-7) × (-7) = 49 as well, because the product of two negative numbers is positive. Thus, -7 is also a square root of 49.
The correct square roots of 49 from the given options are C. [tex]$49^{1 / 2}$[/tex], D. 7, and F. -7.
A number is a square root of another number if, when it is multiplied by itself, it equals the original number. In this case, we're looking for numbers that, when squared, equal 49.
Let's analyze each option:
A. 28:
- If we square 28 (28 × 28), the result is 784, not 49. Therefore, 28 is not a square root of 49.
B. [tex]$-49^{1 / 2}$[/tex]:
- The expression [tex]$49^{1 / 2}$[/tex] indicates taking the square root of 49. In this context, however, the use of `-49` inside a square root suggests a complex or undefined value, so this is not a valid interpretation for our purpose.
C. [tex]$49^{1 / 2}$[/tex]:
- [tex]$49^{1 / 2}$[/tex] means the positive square root of 49. So, it is indeed a square root of 49.
D. 7:
- 7 × 7 = 49, so 7 is a square root of 49.
E. 8:
- 8 × 8 = 64, which does not equal 49. Thus, 8 is not a square root of 49.
F. -7:
- (-7) × (-7) = 49 as well, because the product of two negative numbers is positive. Thus, -7 is also a square root of 49.
The correct square roots of 49 from the given options are C. [tex]$49^{1 / 2}$[/tex], D. 7, and F. -7.
