IdeasCuriosas - Every Question Deserves an Answer Logo

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 .
;

Answered by Anonymous | 2025-07-04

Related Questions in Mathematics

[Answered] Select the correct answer. Which equation is equivalent to the given equation? [tex]$x^2-6 x=8$[/tex] A. [tex]$(x-6)^2=44$[/tex] B. [tex]$(x-3)^2=17$[/tex] C. [tex]$(x-6)^2=20$[/tex] D. [tex]$(x-3)^2=14$[/tex]

[Answered] Which phrase best describes the translation from the graph [tex]y=6 x^2[/tex] to the graph of [tex]y=6(x+1)^2[/tex]? A. 6 units left B. 6 units right C. 1 unit left D. 1 unit right

[Answered] What expression is equivalent to [tex]$\left(5 z^2+3 z+2\right)^2$[/tex] ? A. [tex]$5 z^4+3 z^2+4$[/tex] B. [tex]$5 z^4+9 z^2+4$[/tex] C. [tex]$25 z^4+30 z^3+19 z^2+12 z+4$[/tex] D. [tex]$25 z^4+30 z^3+29 z^2+12 z+4$[/tex]

[Answered] The graph of [tex]y=\frac{5}{4} x+1[/tex] is shown below. The coordinate ([tex]0, y[/tex]) is a solution of the equation. Given the [tex]x[/tex]-value of 0, what is the value of the [tex]y[/tex]-coordinate for the coordinate ([tex]0, y[/tex])? [tex]y=[/tex] [blank]

[Answered] If [tex]f(-2)=0[/tex], what are all the factors of the function [tex]f(x)=x^3-2 x^2-68 x-120[/tex]? Use the Remainder Theorem. A. [tex](x+2)(x+60)[/tex] B. [tex](x-2)(x-60)[/tex] C. [tex](x-10)(x+2)(x+6)[/tex] D. [tex](x+10)(x-2)(x-6)[/tex]