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In Mathematics / High School | 2025-07-03

Which represents a perfect cube?
[tex]$8 \cdot 8 \cdot 8$[/tex]
[tex]$8+8+8$[/tex]
[tex]$9 \cdot 9 \cdot 9 \cdot 9$[/tex]
[tex]$9+9+9+9+9$[/tex]

Asked by caydencole0414

Answer (2)

Evaluate each expression: 8 c d o t 8 c d o t 8 = 512 , 8 + 8 + 8 = 24 , 9 c d o t 9 c d o t 9 c d o t 9 = 6561 , 9 + 9 + 9 + 9 + 9 = 45 .
Check if each result is a perfect cube.
Only 512 is a perfect cube since 8 3 = 512 .
Therefore, the expression that represents a perfect cube is 8 c d o t 8 c d o t 8 ​ .

Explanation

Understanding Perfect Cubes We need to determine which of the given expressions represents a perfect cube. A perfect cube is a number that can be obtained by cubing an integer.

Evaluating the Expressions Let's evaluate each expression:

8 c d o t 8 c d o t 8 = 8 3 = 512 . We need to check if 512 is a perfect cube. Since 8 3 = 512 , 512 is a perfect cube.

8 + 8 + 8 = 3 c d o t 8 = 24 . We need to check if 24 is a perfect cube. The cube root of 24 is not an integer, so 24 is not a perfect cube.

9 c d o t 9 c d o t 9 c d o t 9 = 9 4 = 6561 . We need to check if 6561 is a perfect cube. The cube root of 6561 is not an integer, so 6561 is not a perfect cube.

9 + 9 + 9 + 9 + 9 = 5 c d o t 9 = 45 . We need to check if 45 is a perfect cube. The cube root of 45 is not an integer, so 45 is not a perfect cube.

Identifying the Perfect Cube From the above calculations, only 8 c d o t 8 c d o t 8 = 512 is a perfect cube.

Final Answer Therefore, the expression that represents a perfect cube is 8 c d o t 8 c d o t 8 .


Examples
Perfect cubes are useful in various real-world applications, such as calculating the volume of a cube. For instance, if you are designing a cubic storage container and you want its volume to be a perfect cube for aesthetic or practical reasons, understanding perfect cubes helps you determine the side length needed to achieve that volume. If you want a volume of 512 cubic inches, knowing that 512 is a perfect cube ( 8 3 ) tells you that each side of the container should be 8 inches long. This concept extends to other fields like architecture and engineering, where cubic shapes and volumes are frequently encountered.

Answered by GinnyAnswer | 2025-07-03

The expression that represents a perfect cube is 8 ⋅ 8 ⋅ 8 , which evaluates to 512, as it equals 8 3 . Other expressions do not result in perfect cubes. Therefore, the correct answer is 8 ⋅ 8 ⋅ 8 .
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Answered by Anonymous | 2025-07-04

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