Answer :
To determine which options are square roots of the number 576, we need to consider both the positive and the negative square roots. A square root of a number [tex]\( x \)[/tex] is a number [tex]\( y \)[/tex] such that [tex]\( y^2 = x \)[/tex].
The number 576 can have two square roots: the positive and the negative root.
1. Calculate the positive square root of 576:
- We know that the positive square root of 576 is 24 since [tex]\( 24 \times 24 = 576 \)[/tex].
2. Calculate the negative square root of 576:
- The negative square root is simply the negative of the positive root. Therefore, the negative square root is [tex]\(-24\)[/tex].
Now let's evaluate each option:
- Option A: 24
- This is correct because 24 is the positive square root of 576.
- Option B: -24
- This is correct because -24 is the negative square root of 576.
- Option C: [tex]\( \sqrt{576} \)[/tex]
- This represents the positive square root of 576, which is correct (24).
- Option D: 12
- 12 is not correct because [tex]\( 12 \times 12 = 144\)[/tex], not 576.
- Option E: [tex]\(-\sqrt{576}\)[/tex]
- This represents the negative square root of 576, which is correct (-24).
- Option F: 48
- 48 is not correct because [tex]\( 48 \times 48 = 2304\)[/tex], not 576.
Therefore, the square roots of 576 from the options given are A (24), B (-24), C ([tex]\(\sqrt{576}\)[/tex]), and E ([tex]\(-\sqrt{576}\)[/tex]).
The number 576 can have two square roots: the positive and the negative root.
1. Calculate the positive square root of 576:
- We know that the positive square root of 576 is 24 since [tex]\( 24 \times 24 = 576 \)[/tex].
2. Calculate the negative square root of 576:
- The negative square root is simply the negative of the positive root. Therefore, the negative square root is [tex]\(-24\)[/tex].
Now let's evaluate each option:
- Option A: 24
- This is correct because 24 is the positive square root of 576.
- Option B: -24
- This is correct because -24 is the negative square root of 576.
- Option C: [tex]\( \sqrt{576} \)[/tex]
- This represents the positive square root of 576, which is correct (24).
- Option D: 12
- 12 is not correct because [tex]\( 12 \times 12 = 144\)[/tex], not 576.
- Option E: [tex]\(-\sqrt{576}\)[/tex]
- This represents the negative square root of 576, which is correct (-24).
- Option F: 48
- 48 is not correct because [tex]\( 48 \times 48 = 2304\)[/tex], not 576.
Therefore, the square roots of 576 from the options given are A (24), B (-24), C ([tex]\(\sqrt{576}\)[/tex]), and E ([tex]\(-\sqrt{576}\)[/tex]).
