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Answer :
Sure, let me guide you through the question and identify which items are equivalent to [tex]\(\sqrt{24}\)[/tex].
1. Understanding [tex]\(\sqrt{24}\)[/tex]:
- [tex]\(\sqrt{24}\)[/tex] means finding a number that, when multiplied by itself, gives 24. It represents the positive number [tex]\(x\)[/tex] for which [tex]\(x \cdot x = 24\)[/tex].
Now, let's evaluate each option to see which ones match this concept:
a. The area of a square with side length 24 units:
- If a square has a side length of 24 units, its area is [tex]\(24 \cdot 24 = 576\)[/tex].
- This is not equivalent to [tex]\(\sqrt{24}\)[/tex].
b. The side length of a square with area 24 square units:
- If the area of a square is 24, then the side length is [tex]\(\sqrt{24}\)[/tex].
- This matches the definition of [tex]\(\sqrt{24}\)[/tex].
c. The positive number [tex]\(x\)[/tex], where [tex]\(x \cdot x = 24\)[/tex]:
- This is a direct definition of [tex]\(\sqrt{24}\)[/tex], as [tex]\(x\)[/tex] would be [tex]\(\sqrt{24}\)[/tex].
d. The positive number [tex]\(y\)[/tex], where [tex]\(y = 24 \cdot 24\)[/tex]:
- Here, [tex]\(y\)[/tex] equals 576, which is not [tex]\(\sqrt{24}\)[/tex].
e. The edge length of a cube with volume 24 cubic units:
- The edge length of a cube with volume 24 is [tex]\(\sqrt[3]{24}\)[/tex] (the cube root of 24), not [tex]\(\sqrt{24}\)[/tex].
f. The volume of a cube with edge length 24 units:
- If the edge length is 24, then the volume is [tex]\(24 \cdot 24 \cdot 24 = 24^3\)[/tex], which is much larger than [tex]\(\sqrt{24}\)[/tex].
So, 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]
These are the options equivalent to [tex]\(\sqrt{24}\)[/tex].
1. Understanding [tex]\(\sqrt{24}\)[/tex]:
- [tex]\(\sqrt{24}\)[/tex] means finding a number that, when multiplied by itself, gives 24. It represents the positive number [tex]\(x\)[/tex] for which [tex]\(x \cdot x = 24\)[/tex].
Now, let's evaluate each option to see which ones match this concept:
a. The area of a square with side length 24 units:
- If a square has a side length of 24 units, its area is [tex]\(24 \cdot 24 = 576\)[/tex].
- This is not equivalent to [tex]\(\sqrt{24}\)[/tex].
b. The side length of a square with area 24 square units:
- If the area of a square is 24, then the side length is [tex]\(\sqrt{24}\)[/tex].
- This matches the definition of [tex]\(\sqrt{24}\)[/tex].
c. The positive number [tex]\(x\)[/tex], where [tex]\(x \cdot x = 24\)[/tex]:
- This is a direct definition of [tex]\(\sqrt{24}\)[/tex], as [tex]\(x\)[/tex] would be [tex]\(\sqrt{24}\)[/tex].
d. The positive number [tex]\(y\)[/tex], where [tex]\(y = 24 \cdot 24\)[/tex]:
- Here, [tex]\(y\)[/tex] equals 576, which is not [tex]\(\sqrt{24}\)[/tex].
e. The edge length of a cube with volume 24 cubic units:
- The edge length of a cube with volume 24 is [tex]\(\sqrt[3]{24}\)[/tex] (the cube root of 24), not [tex]\(\sqrt{24}\)[/tex].
f. The volume of a cube with edge length 24 units:
- If the edge length is 24, then the volume is [tex]\(24 \cdot 24 \cdot 24 = 24^3\)[/tex], which is much larger than [tex]\(\sqrt{24}\)[/tex].
So, 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]
These are the options equivalent to [tex]\(\sqrt{24}\)[/tex].
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