Answer :
To determine which items are equivalent to [tex]\(\sqrt{24}\)[/tex], we need to consider what [tex]\(\sqrt{24}\)[/tex] represents. The square root of 24 is the positive number that, when multiplied by itself, equals 24. Let's analyze each choice:
A. The area of a square with side length 24 units:
- If a square has a side length of 24 units, its area would be [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's area is 24 square units, its side length would be [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]:
- The equation [tex]\(x \cdot x = 24\)[/tex] suggests that [tex]\(x\)[/tex] is [tex]\(\sqrt{24}\)[/tex].
- This is equivalent to [tex]\(\sqrt{24}\)[/tex].
D. The positive number [tex]\(y\)[/tex], where [tex]\(y = 24 \cdot 24\)[/tex]:
- If [tex]\(y = 24 \times 24 = 576\)[/tex], which is not equivalent to [tex]\(\sqrt{24}\)[/tex].
E. The edge length of a cube with volume 24 cubic units:
- If a cube's volume is 24 cubic units, the edge length is the cube root of 24, i.e., [tex]\(\sqrt[3]{24}\)[/tex].
- This is not equivalent to [tex]\(\sqrt{24}\)[/tex].
F. The volume of a cube with edge length 24 units:
- If a cube has an edge length of 24 units, its volume is [tex]\(24^3 = 13,824\)[/tex] cubic units.
- This is not equivalent to [tex]\(\sqrt{24}\)[/tex].
Based on the analysis, 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].
A. The area of a square with side length 24 units:
- If a square has a side length of 24 units, its area would be [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's area is 24 square units, its side length would be [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]:
- The equation [tex]\(x \cdot x = 24\)[/tex] suggests that [tex]\(x\)[/tex] is [tex]\(\sqrt{24}\)[/tex].
- This is equivalent to [tex]\(\sqrt{24}\)[/tex].
D. The positive number [tex]\(y\)[/tex], where [tex]\(y = 24 \cdot 24\)[/tex]:
- If [tex]\(y = 24 \times 24 = 576\)[/tex], which is not equivalent to [tex]\(\sqrt{24}\)[/tex].
E. The edge length of a cube with volume 24 cubic units:
- If a cube's volume is 24 cubic units, the edge length is the cube root of 24, i.e., [tex]\(\sqrt[3]{24}\)[/tex].
- This is not equivalent to [tex]\(\sqrt{24}\)[/tex].
F. The volume of a cube with edge length 24 units:
- If a cube has an edge length of 24 units, its volume is [tex]\(24^3 = 13,824\)[/tex] cubic units.
- This is not equivalent to [tex]\(\sqrt{24}\)[/tex].
Based on the analysis, 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].
