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Answer :
To determine which items are equivalent to [tex]\(\sqrt{24}\)[/tex], let's evaluate each statement one by one:
A. The area of a square with side length 24 units:
- The area of a square is calculated as side length squared, [tex]\(24 \times 24 = 576\)[/tex].
- [tex]\(\sqrt{24}\)[/tex] is not equivalent to 576.
B. The side length of a square with area 24 square units:
- To find the side length of such a square, use [tex]\(\sqrt{24}\)[/tex].
- This statement is equivalent to [tex]\(\sqrt{24}\)[/tex].
C. The positive number [tex]\(x\)[/tex], where [tex]\(x \cdot x = 24\)[/tex]:
- This statement essentially asks for the square root of 24.
- Therefore, this is equivalent to [tex]\(\sqrt{24}\)[/tex].
D. The positive number [tex]\(y\)[/tex], where [tex]\(y = 24 \cdot 24\)[/tex]:
- This is equivalent to 576, which is definitely not [tex]\(\sqrt{24}\)[/tex].
E. The edge length of a cube with volume 24 cubic units:
- The edge length is the cube root of 24, which is not [tex]\(\sqrt{24}\)[/tex].
F. The volume of a cube with edge length 24 units:
- The volume is [tex]\(24^3\)[/tex], which is 13,824, and not [tex]\(\sqrt{24}\)[/tex].
Based on this breakdown, items B and C are equivalent to [tex]\(\sqrt{24}\)[/tex].
A. The area of a square with side length 24 units:
- The area of a square is calculated as side length squared, [tex]\(24 \times 24 = 576\)[/tex].
- [tex]\(\sqrt{24}\)[/tex] is not equivalent to 576.
B. The side length of a square with area 24 square units:
- To find the side length of such a square, use [tex]\(\sqrt{24}\)[/tex].
- This statement is equivalent to [tex]\(\sqrt{24}\)[/tex].
C. The positive number [tex]\(x\)[/tex], where [tex]\(x \cdot x = 24\)[/tex]:
- This statement essentially asks for the square root of 24.
- Therefore, this is equivalent to [tex]\(\sqrt{24}\)[/tex].
D. The positive number [tex]\(y\)[/tex], where [tex]\(y = 24 \cdot 24\)[/tex]:
- This is equivalent to 576, which is definitely not [tex]\(\sqrt{24}\)[/tex].
E. The edge length of a cube with volume 24 cubic units:
- The edge length is the cube root of 24, which is not [tex]\(\sqrt{24}\)[/tex].
F. The volume of a cube with edge length 24 units:
- The volume is [tex]\(24^3\)[/tex], which is 13,824, and not [tex]\(\sqrt{24}\)[/tex].
Based on this breakdown, items B and C are equivalent to [tex]\(\sqrt{24}\)[/tex].
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