Answer :
Sure! Let's break down the problem step-by-step to identify which items are equivalent to [tex]\(\sqrt{24}\)[/tex].
1. 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.
- Since [tex]\(\sqrt{24} \approx 4.9\)[/tex] does not equal 576, this is not equivalent.
2. The side length of a square with area 24 square units:
- If a square has an area of 24 square units, its side length would be [tex]\(\sqrt{24}\)[/tex], which is approximately 4.9 units.
- Therefore, this is equivalent to [tex]\(\sqrt{24}\)[/tex].
3. The edge length of a cube with volume 24 cubic units:
- If the volume of a cube is 24 cubic units, the edge length would be [tex]\(\sqrt[3]{24}\)[/tex], which is not [tex]\(\sqrt{24}\)[/tex].
- Hence, this is not equivalent.
4. The volume of a cube with edge length 24 units:
- If a cube has an edge length of 24 units, its volume would be [tex]\(24 \times 24 \times 24 = 13,824\)[/tex] cubic units.
- Since [tex]\(\sqrt{24}\)[/tex] is much smaller than 13,824, this is not equivalent.
5. The positive number x, where [tex]\(x \cdot x = 24\)[/tex]:
- If [tex]\(x \cdot x = 24\)[/tex], then [tex]\(x = \sqrt{24}\)[/tex].
- This matches the value we're looking for, so it is equivalent.
6. The positive number y, where [tex]\(y = 24 \cdot 24\)[/tex]:
- If [tex]\(y = 24 \times 24\)[/tex], then [tex]\(y = 576\)[/tex].
- Since [tex]\(\sqrt{24}\)[/tex] is approximately 4.9, not 576, this is not equivalent.
Thus, the items equivalent to [tex]\(\sqrt{24}\)[/tex] are:
- The side length of a square with area 24 square units
- The positive number x, where [tex]\(x \cdot x = 24\)[/tex]
1. 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.
- Since [tex]\(\sqrt{24} \approx 4.9\)[/tex] does not equal 576, this is not equivalent.
2. The side length of a square with area 24 square units:
- If a square has an area of 24 square units, its side length would be [tex]\(\sqrt{24}\)[/tex], which is approximately 4.9 units.
- Therefore, this is equivalent to [tex]\(\sqrt{24}\)[/tex].
3. The edge length of a cube with volume 24 cubic units:
- If the volume of a cube is 24 cubic units, the edge length would be [tex]\(\sqrt[3]{24}\)[/tex], which is not [tex]\(\sqrt{24}\)[/tex].
- Hence, this is not equivalent.
4. The volume of a cube with edge length 24 units:
- If a cube has an edge length of 24 units, its volume would be [tex]\(24 \times 24 \times 24 = 13,824\)[/tex] cubic units.
- Since [tex]\(\sqrt{24}\)[/tex] is much smaller than 13,824, this is not equivalent.
5. The positive number x, where [tex]\(x \cdot x = 24\)[/tex]:
- If [tex]\(x \cdot x = 24\)[/tex], then [tex]\(x = \sqrt{24}\)[/tex].
- This matches the value we're looking for, so it is equivalent.
6. The positive number y, where [tex]\(y = 24 \cdot 24\)[/tex]:
- If [tex]\(y = 24 \times 24\)[/tex], then [tex]\(y = 576\)[/tex].
- Since [tex]\(\sqrt{24}\)[/tex] is approximately 4.9, not 576, this is not equivalent.
Thus, the items equivalent to [tex]\(\sqrt{24}\)[/tex] are:
- The side length of a square with area 24 square units
- The positive number x, where [tex]\(x \cdot x = 24\)[/tex]
