Answer :
Let's determine which items are equivalent to [tex]\(\sqrt{24}\)[/tex].
1. Option a: The area of a square with side length 24 units.
- The area of a square with side length 24 is calculated as [tex]\(24 \times 24 = 576\)[/tex]. This is not related to [tex]\(\sqrt{24}\)[/tex].
2. Option b: The side length of a square with area 24 square units.
- For a square with an area of 24, the side length would be [tex]\(\sqrt{24}\)[/tex], which matches the expression we are looking for.
3. Option c: The positive number [tex]\(x\)[/tex], where [tex]\(x \cdot x = 24\)[/tex].
- Solving the equation [tex]\(x^2 = 24\)[/tex] gives [tex]\(x = \sqrt{24}\)[/tex]. This is equivalent to [tex]\(\sqrt{24}\)[/tex].
4. Option d: The positive number [tex]\(y\)[/tex], where [tex]\(y = 24 \cdot 24\)[/tex].
- Here, [tex]\(y = 576\)[/tex], which is not related to [tex]\(\sqrt{24}\)[/tex].
5. Option e: The edge length of a cube with volume 24 cubic units.
- To find the edge length [tex]\(e\)[/tex] of a cube with volume 24, we solve [tex]\(e^3 = 24\)[/tex]. This gives [tex]\(e = \sqrt[3]{24}\)[/tex], which is not equivalent to [tex]\(\sqrt{24}\)[/tex].
6. Option f: The volume of a cube with edge length 24 units.
- The volume of a cube with edge length 24 is [tex]\(24 \times 24 \times 24 = 13824\)[/tex], which is nowhere close to [tex]\(\sqrt{24}\)[/tex].
Given the analysis, 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].
1. Option a: The area of a square with side length 24 units.
- The area of a square with side length 24 is calculated as [tex]\(24 \times 24 = 576\)[/tex]. This is not related to [tex]\(\sqrt{24}\)[/tex].
2. Option b: The side length of a square with area 24 square units.
- For a square with an area of 24, the side length would be [tex]\(\sqrt{24}\)[/tex], which matches the expression we are looking for.
3. Option c: The positive number [tex]\(x\)[/tex], where [tex]\(x \cdot x = 24\)[/tex].
- Solving the equation [tex]\(x^2 = 24\)[/tex] gives [tex]\(x = \sqrt{24}\)[/tex]. This is equivalent to [tex]\(\sqrt{24}\)[/tex].
4. Option d: The positive number [tex]\(y\)[/tex], where [tex]\(y = 24 \cdot 24\)[/tex].
- Here, [tex]\(y = 576\)[/tex], which is not related to [tex]\(\sqrt{24}\)[/tex].
5. Option e: The edge length of a cube with volume 24 cubic units.
- To find the edge length [tex]\(e\)[/tex] of a cube with volume 24, we solve [tex]\(e^3 = 24\)[/tex]. This gives [tex]\(e = \sqrt[3]{24}\)[/tex], which is not equivalent to [tex]\(\sqrt{24}\)[/tex].
6. Option f: The volume of a cube with edge length 24 units.
- The volume of a cube with edge length 24 is [tex]\(24 \times 24 \times 24 = 13824\)[/tex], which is nowhere close to [tex]\(\sqrt{24}\)[/tex].
Given the analysis, 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].
