Answer :
To find the square roots of the number 49, let's go through each option and see which ones are square roots of 49:
1. Understanding Square Roots:
- The square root of a number [tex]\( x \)[/tex] is a number [tex]\( y \)[/tex] such that [tex]\( y \times y = x \)[/tex].
- For 49, we are looking for numbers that satisfy the equation [tex]\( y \times y = 49 \)[/tex].
2. Checking Each Option:
- Option A: 28
- [tex]\( 28 \times 28 = 784 \)[/tex], which is not equal to 49. So, 28 is not a square root of 49.
- Option B: [tex]\( 49^{1/2} \)[/tex]
- [tex]\( 49^{1/2} \)[/tex] is mathematically defined as the positive square root of 49.
- [tex]\( 49^{1/2} = 7 \)[/tex], thus it is a square root of 49.
- Option C: 7
- [tex]\( 7 \times 7 = 49 \)[/tex], so 7 is indeed a square root of 49.
- Option D: -7
- [tex]\( (-7) \times (-7) = 49 \)[/tex], therefore, -7 is also a square root of 49.
- Option E: 8
- [tex]\( 8 \times 8 = 64 \)[/tex], which is not equal to 49. So, 8 is not a square root of 49.
- Option F: [tex]\(-49^{1/2}\)[/tex]
- [tex]\(-49^{1/2}\)[/tex] is mathematically defined as the negative square root of 49.
- [tex]\(-49^{1/2} = -7\)[/tex], so it is a square root of 49.
3. Conclusion:
- The correct answers, or the numbers that are square roots of 49, are:
- B. [tex]\( 49^{1/2} \)[/tex]
- C. 7
- D. -7
- F. [tex]\(-49^{1/2}\)[/tex]
These options accurately represent the square roots of 49, which are 7 and -7.
1. Understanding Square Roots:
- The square root of a number [tex]\( x \)[/tex] is a number [tex]\( y \)[/tex] such that [tex]\( y \times y = x \)[/tex].
- For 49, we are looking for numbers that satisfy the equation [tex]\( y \times y = 49 \)[/tex].
2. Checking Each Option:
- Option A: 28
- [tex]\( 28 \times 28 = 784 \)[/tex], which is not equal to 49. So, 28 is not a square root of 49.
- Option B: [tex]\( 49^{1/2} \)[/tex]
- [tex]\( 49^{1/2} \)[/tex] is mathematically defined as the positive square root of 49.
- [tex]\( 49^{1/2} = 7 \)[/tex], thus it is a square root of 49.
- Option C: 7
- [tex]\( 7 \times 7 = 49 \)[/tex], so 7 is indeed a square root of 49.
- Option D: -7
- [tex]\( (-7) \times (-7) = 49 \)[/tex], therefore, -7 is also a square root of 49.
- Option E: 8
- [tex]\( 8 \times 8 = 64 \)[/tex], which is not equal to 49. So, 8 is not a square root of 49.
- Option F: [tex]\(-49^{1/2}\)[/tex]
- [tex]\(-49^{1/2}\)[/tex] is mathematically defined as the negative square root of 49.
- [tex]\(-49^{1/2} = -7\)[/tex], so it is a square root of 49.
3. Conclusion:
- The correct answers, or the numbers that are square roots of 49, are:
- B. [tex]\( 49^{1/2} \)[/tex]
- C. 7
- D. -7
- F. [tex]\(-49^{1/2}\)[/tex]
These options accurately represent the square roots of 49, which are 7 and -7.
