Answer :
To determine which items are equivalent to [tex]\(\sqrt{24}\)[/tex], let's analyze each given option:
1. The positive number [tex]\(x\)[/tex], where [tex]\(x \times x = 24\)[/tex]:
- This is equivalent to [tex]\(\sqrt{24}\)[/tex] because the definition of the square root of a number [tex]\(n\)[/tex] is the value [tex]\(x\)[/tex] such that [tex]\(x \times x = n\)[/tex].
2. The positive number [tex]\(y\)[/tex], where [tex]\(y = 24 \times 24\)[/tex]:
- This is not equivalent to [tex]\(\sqrt{24}\)[/tex]. Instead, this calculation results in [tex]\(y = 576\)[/tex], which is [tex]\(24^2\)[/tex], not the square root.
3. The volume of a cube with edge length 24 units:
- The volume of a cube with edge length 24 is [tex]\(24^3\)[/tex], which is [tex]\(13,824\)[/tex]. This is not equivalent to [tex]\(\sqrt{24}\)[/tex].
4. The edge length of a cube with volume 24 cubic units:
- To find the edge length of a cube with a volume of 24, we solve [tex]\(s^3 = 24\)[/tex] to find [tex]\(s\)[/tex]. The edge length [tex]\(s\)[/tex] is the cube root of 24, which is not [tex]\(\sqrt{24}\)[/tex] but has a similar solving process as finding [tex]\(\sqrt{24}\)[/tex].
5. The area of a square with side length 24 units:
- The area of a square with side length 24 is [tex]\(24^2 = 576\)[/tex]. This is not equivalent to [tex]\(\sqrt{24}\)[/tex].
6. The side length of a square with area 24 square units:
- If the area of a square is 24, then the side length [tex]\(s\)[/tex] satisfies [tex]\(s \times s = 24\)[/tex]. This is equivalent to [tex]\(\sqrt{24}\)[/tex].
Therefore, the items that are equivalent to [tex]\(\sqrt{24}\)[/tex] are those with options 1 and 6. In this exercise, the given results treated all the necessary intersections correctly.
1. The positive number [tex]\(x\)[/tex], where [tex]\(x \times x = 24\)[/tex]:
- This is equivalent to [tex]\(\sqrt{24}\)[/tex] because the definition of the square root of a number [tex]\(n\)[/tex] is the value [tex]\(x\)[/tex] such that [tex]\(x \times x = n\)[/tex].
2. The positive number [tex]\(y\)[/tex], where [tex]\(y = 24 \times 24\)[/tex]:
- This is not equivalent to [tex]\(\sqrt{24}\)[/tex]. Instead, this calculation results in [tex]\(y = 576\)[/tex], which is [tex]\(24^2\)[/tex], not the square root.
3. The volume of a cube with edge length 24 units:
- The volume of a cube with edge length 24 is [tex]\(24^3\)[/tex], which is [tex]\(13,824\)[/tex]. This is not equivalent to [tex]\(\sqrt{24}\)[/tex].
4. The edge length of a cube with volume 24 cubic units:
- To find the edge length of a cube with a volume of 24, we solve [tex]\(s^3 = 24\)[/tex] to find [tex]\(s\)[/tex]. The edge length [tex]\(s\)[/tex] is the cube root of 24, which is not [tex]\(\sqrt{24}\)[/tex] but has a similar solving process as finding [tex]\(\sqrt{24}\)[/tex].
5. The area of a square with side length 24 units:
- The area of a square with side length 24 is [tex]\(24^2 = 576\)[/tex]. This is not equivalent to [tex]\(\sqrt{24}\)[/tex].
6. The side length of a square with area 24 square units:
- If the area of a square is 24, then the side length [tex]\(s\)[/tex] satisfies [tex]\(s \times s = 24\)[/tex]. This is equivalent to [tex]\(\sqrt{24}\)[/tex].
Therefore, the items that are equivalent to [tex]\(\sqrt{24}\)[/tex] are those with options 1 and 6. In this exercise, the given results treated all the necessary intersections correctly.
