High School

Select all items equivalent to [tex]\sqrt{24}[/tex].

A. The area of a square with side length 24 units
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]
D. The positive number [tex]y[/tex], where [tex]y = 24 \cdot 24[/tex]
E. The edge length of a cube with volume 24 cubic units
F. The volume of a cube with edge length 24 units

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].