Answer :
To solve the problem of identifying which items are equivalent to [tex]\(\sqrt{24}\)[/tex], let's evaluate each of the options:
- A. The area of a square with side length 24 units
The area of a square is calculated as the side length squared:
[tex]\(24 \times 24 = 576\)[/tex].
This is not equivalent to [tex]\(\sqrt{24}\)[/tex].
- B. The side length of a square with area 24 square units
To find the side length of a square when the area is 24, you take the square root of 24:
[tex]\(\sqrt{24}\)[/tex].
This is equivalent to [tex]\(\sqrt{24}\)[/tex].
- C. The positive number [tex]\(x\)[/tex], where [tex]\(x \cdot x = 24\)[/tex]
Solving for [tex]\(x\)[/tex] gives us [tex]\(x = \sqrt{24}\)[/tex].
This is equivalent to [tex]\(\sqrt{24}\)[/tex].
- D. The positive number [tex]\(y\)[/tex], where [tex]\(y = 24 \cdot 24\)[/tex]
This results in [tex]\(y = 576\)[/tex].
This is not equivalent to [tex]\(\sqrt{24}\)[/tex].
- E. The edge length of a cube with volume 24 cubic units
To find the edge length of a cube when the volume is 24, you find the cube root of 24, which is not equivalent to [tex]\(\sqrt{24}\)[/tex].
- F. The volume of a cube with edge length 24 units
The volume of a cube is given by the cube of the edge length:
[tex]\(24^3 = 13824\)[/tex].
This is not equivalent to [tex]\(\sqrt{24}\)[/tex].
Based on this evaluation, the items equivalent to [tex]\(\sqrt{24}\)[/tex] are:
- B. The side length of a square with area 24 square units
- C. The positive number [tex]\(x\)[/tex], where [tex]\(x \cdot x = 24\)[/tex]
These choices both relate directly to the expression [tex]\(\sqrt{24}\)[/tex].
- A. The area of a square with side length 24 units
The area of a square is calculated as the side length squared:
[tex]\(24 \times 24 = 576\)[/tex].
This is not equivalent to [tex]\(\sqrt{24}\)[/tex].
- B. The side length of a square with area 24 square units
To find the side length of a square when the area is 24, you take the square root of 24:
[tex]\(\sqrt{24}\)[/tex].
This is equivalent to [tex]\(\sqrt{24}\)[/tex].
- C. The positive number [tex]\(x\)[/tex], where [tex]\(x \cdot x = 24\)[/tex]
Solving for [tex]\(x\)[/tex] gives us [tex]\(x = \sqrt{24}\)[/tex].
This is equivalent to [tex]\(\sqrt{24}\)[/tex].
- D. The positive number [tex]\(y\)[/tex], where [tex]\(y = 24 \cdot 24\)[/tex]
This results in [tex]\(y = 576\)[/tex].
This is not equivalent to [tex]\(\sqrt{24}\)[/tex].
- E. The edge length of a cube with volume 24 cubic units
To find the edge length of a cube when the volume is 24, you find the cube root of 24, which is not equivalent to [tex]\(\sqrt{24}\)[/tex].
- F. The volume of a cube with edge length 24 units
The volume of a cube is given by the cube of the edge length:
[tex]\(24^3 = 13824\)[/tex].
This is not equivalent to [tex]\(\sqrt{24}\)[/tex].
Based on this evaluation, the items equivalent to [tex]\(\sqrt{24}\)[/tex] are:
- B. The side length of a square with area 24 square units
- C. The positive number [tex]\(x\)[/tex], where [tex]\(x \cdot x = 24\)[/tex]
These choices both relate directly to the expression [tex]\(\sqrt{24}\)[/tex].
