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Answer :
To solve this problem, we need to determine which statements are equivalent to [tex]\(\sqrt{24}\)[/tex].
Let's analyze each option:
A. The area of a square with side length 24 units:
- If a square has a side length of 24 units, its area is calculated by [tex]\(24 \times 24 = 576\)[/tex] square units.
- This is not equivalent to [tex]\(\sqrt{24}\)[/tex].
B. The side length of a square with area 24 square units:
- If a square has an area of 24 square units, the side length can be found by taking the square root of 24, which is [tex]\(\sqrt{24}\)[/tex].
- This option is equivalent to [tex]\(\sqrt{24}\)[/tex].
C. The positive number [tex]\(x\)[/tex], where [tex]\(x \cdot x = 24\)[/tex]:
- The equation [tex]\(x \cdot x = 24\)[/tex] simplifies to [tex]\(x = \sqrt{24}\)[/tex].
- This means [tex]\(x\)[/tex] is equivalent to [tex]\(\sqrt{24}\)[/tex].
D. The positive number [tex]\(y\)[/tex], where [tex]\(y = 24 \cdot 24\)[/tex]:
- Here, [tex]\(y = 576\)[/tex], since [tex]\(24 \times 24 = 576\)[/tex].
- This is not equivalent to [tex]\(\sqrt{24}\)[/tex].
E. The edge length of a cube with volume 24 cubic units:
- The volume of a cube is calculated as [tex]\( \text{edge length}^3 = \text{volume} \)[/tex].
- To find the edge length for a cube with a volume of 24, you take the cube root: [tex]\(\sqrt[3]{24}\)[/tex].
- [tex]\(\sqrt[3]{24}\)[/tex] is not equal to [tex]\(\sqrt{24}\)[/tex].
F. The volume of a cube with edge length 24 units:
- The volume of a cube with edge length 24 units is [tex]\(24^3 = 13,824\)[/tex] cubic units.
- This is not equivalent to [tex]\(\sqrt{24}\)[/tex].
Therefore, the items that are 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]
Let's analyze each option:
A. The area of a square with side length 24 units:
- If a square has a side length of 24 units, its area is calculated by [tex]\(24 \times 24 = 576\)[/tex] square units.
- This is not equivalent to [tex]\(\sqrt{24}\)[/tex].
B. The side length of a square with area 24 square units:
- If a square has an area of 24 square units, the side length can be found by taking the square root of 24, which is [tex]\(\sqrt{24}\)[/tex].
- This option is equivalent to [tex]\(\sqrt{24}\)[/tex].
C. The positive number [tex]\(x\)[/tex], where [tex]\(x \cdot x = 24\)[/tex]:
- The equation [tex]\(x \cdot x = 24\)[/tex] simplifies to [tex]\(x = \sqrt{24}\)[/tex].
- This means [tex]\(x\)[/tex] is equivalent to [tex]\(\sqrt{24}\)[/tex].
D. The positive number [tex]\(y\)[/tex], where [tex]\(y = 24 \cdot 24\)[/tex]:
- Here, [tex]\(y = 576\)[/tex], since [tex]\(24 \times 24 = 576\)[/tex].
- This is not equivalent to [tex]\(\sqrt{24}\)[/tex].
E. The edge length of a cube with volume 24 cubic units:
- The volume of a cube is calculated as [tex]\( \text{edge length}^3 = \text{volume} \)[/tex].
- To find the edge length for a cube with a volume of 24, you take the cube root: [tex]\(\sqrt[3]{24}\)[/tex].
- [tex]\(\sqrt[3]{24}\)[/tex] is not equal to [tex]\(\sqrt{24}\)[/tex].
F. The volume of a cube with edge length 24 units:
- The volume of a cube with edge length 24 units is [tex]\(24^3 = 13,824\)[/tex] cubic units.
- This is not equivalent to [tex]\(\sqrt{24}\)[/tex].
Therefore, the items that are 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]
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