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Answer :
- Square roots of a number are values that, when squared, equal the original number.
- Check each option by squaring it to see if it equals 576.
- 24 squared is 576, so 24 is a square root.
- -24 squared is 576, so -24 is a square root.
- $576^{1/2}$ is 24, so it is a square root.
- $-576^{1/2}$ is -24, so it is a square root.
- The square roots of 576 are 24, $576^{1 / 2}$, -24, and $-576^{1 / 2}$.
- The final answer is A, C, E, F.
### Explanation
1. Understanding Square Roots
We are asked to identify the square roots of 576 from the given options. A square root of a number is a value that, when multiplied by itself, gives the original number.
2. Checking Each Option
Let's examine each option:
A. 24: $24 \times 24 = 576$. So, 24 is a square root of 576.
B. 48: $48 \times 48 = 2304$. So, 48 is not a square root of 576.
C. $576^{1 / 2}$: This represents the principal square root of 576, which is 24. So, $576^{1 / 2}$ is a square root of 576.
D. 12: $12 \times 12 = 144$. So, 12 is not a square root of 576.
E. -24: $(-24) \times (-24) = 576$. So, -24 is a square root of 576.
F. $-576^{1 / 2}$: This represents the negative of the principal square root of 576, which is -24. So, $-576^{1 / 2}$ is a square root of 576.
3. Identifying the Correct Options
Therefore, the square roots of 576 from the given options are 24, $576^{1 / 2}$, -24, and $-576^{1 / 2}$.
### Examples
Square roots are used in various real-life applications, such as calculating the length of the side of a square given its area, determining distances in geometry, and solving physics problems involving motion and energy. For instance, if you have a square garden with an area of 576 square feet, finding the square root of 576 tells you that each side of the garden is 24 feet long. Understanding square roots helps in practical measurements and calculations.
- Check each option by squaring it to see if it equals 576.
- 24 squared is 576, so 24 is a square root.
- -24 squared is 576, so -24 is a square root.
- $576^{1/2}$ is 24, so it is a square root.
- $-576^{1/2}$ is -24, so it is a square root.
- The square roots of 576 are 24, $576^{1 / 2}$, -24, and $-576^{1 / 2}$.
- The final answer is A, C, E, F.
### Explanation
1. Understanding Square Roots
We are asked to identify the square roots of 576 from the given options. A square root of a number is a value that, when multiplied by itself, gives the original number.
2. Checking Each Option
Let's examine each option:
A. 24: $24 \times 24 = 576$. So, 24 is a square root of 576.
B. 48: $48 \times 48 = 2304$. So, 48 is not a square root of 576.
C. $576^{1 / 2}$: This represents the principal square root of 576, which is 24. So, $576^{1 / 2}$ is a square root of 576.
D. 12: $12 \times 12 = 144$. So, 12 is not a square root of 576.
E. -24: $(-24) \times (-24) = 576$. So, -24 is a square root of 576.
F. $-576^{1 / 2}$: This represents the negative of the principal square root of 576, which is -24. So, $-576^{1 / 2}$ is a square root of 576.
3. Identifying the Correct Options
Therefore, the square roots of 576 from the given options are 24, $576^{1 / 2}$, -24, and $-576^{1 / 2}$.
### Examples
Square roots are used in various real-life applications, such as calculating the length of the side of a square given its area, determining distances in geometry, and solving physics problems involving motion and energy. For instance, if you have a square garden with an area of 576 square feet, finding the square root of 576 tells you that each side of the garden is 24 feet long. Understanding square roots helps in practical measurements and calculations.
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