Answer :
To determine which numbers are square roots of 529, we need to recognize that a square root of a number [tex]\( x \)[/tex] is a value [tex]\( y \)[/tex] such that [tex]\( y^2 = x \)[/tex].
Here, we are looking for numbers such that [tex]\( y^2 = 529 \)[/tex].
Let's find the square roots of 529:
1. Calculate the Positive Square Root:
- The positive square root of a number is the number that when multiplied by itself gives the original number.
- For 529, this is 23 because:
[tex]\[
23 \times 23 = 529
\][/tex]
So, 23 is a square root of 529.
2. Calculate the Negative Square Root:
- The negative square root is simply the negative of the positive square root.
- So, [tex]\(-23\)[/tex] is also a square root of 529 because:
[tex]\[
(-23) \times (-23) = 529
\][/tex]
Thus, [tex]\(-23\)[/tex] is another square root of 529.
Now, let's match our findings with the options provided:
- A. 1058: This is not the square root of 529, as it's much larger than 529 itself.
- B. 46: Not the square root, because [tex]\(46 \times 46 = 2116\)[/tex], which is far larger than 529.
- C. [tex]\(-529^{1/2}\)[/tex]: This is another way to say [tex]\(-\sqrt{529}\)[/tex], which equals [tex]\(-23\)[/tex]. Therefore, this is a square root.
- D. 23: As we calculated, 23 is indeed a square root of 529.
- E. [tex]\(529^{1/2}\)[/tex]: This is simply another way of expressing the positive square root, which is 23. So, this is a square root.
- F. -23: We have already determined that [tex]\(-23\)[/tex] is a square root of 529.
Thus, the correct answers are:
- C. [tex]\(-529^{1/2}\)[/tex]
- D. 23
- E. [tex]\(529^{1/2}\)[/tex]
- F. -23
Here, we are looking for numbers such that [tex]\( y^2 = 529 \)[/tex].
Let's find the square roots of 529:
1. Calculate the Positive Square Root:
- The positive square root of a number is the number that when multiplied by itself gives the original number.
- For 529, this is 23 because:
[tex]\[
23 \times 23 = 529
\][/tex]
So, 23 is a square root of 529.
2. Calculate the Negative Square Root:
- The negative square root is simply the negative of the positive square root.
- So, [tex]\(-23\)[/tex] is also a square root of 529 because:
[tex]\[
(-23) \times (-23) = 529
\][/tex]
Thus, [tex]\(-23\)[/tex] is another square root of 529.
Now, let's match our findings with the options provided:
- A. 1058: This is not the square root of 529, as it's much larger than 529 itself.
- B. 46: Not the square root, because [tex]\(46 \times 46 = 2116\)[/tex], which is far larger than 529.
- C. [tex]\(-529^{1/2}\)[/tex]: This is another way to say [tex]\(-\sqrt{529}\)[/tex], which equals [tex]\(-23\)[/tex]. Therefore, this is a square root.
- D. 23: As we calculated, 23 is indeed a square root of 529.
- E. [tex]\(529^{1/2}\)[/tex]: This is simply another way of expressing the positive square root, which is 23. So, this is a square root.
- F. -23: We have already determined that [tex]\(-23\)[/tex] is a square root of 529.
Thus, the correct answers are:
- C. [tex]\(-529^{1/2}\)[/tex]
- D. 23
- E. [tex]\(529^{1/2}\)[/tex]
- F. -23
