Answer:
To determine which number from the given options is a perfect cube, we need to find out if any of the numbers can be expressed as the cube of an integer.
To do this, we need to find the cube root of each number and see if it yields a whole number.
Let's go through each option:
1. Cube root of 648: ∛648 ≈ 8. The cube root of 648 is not a whole number, so it is not a perfect cube.
2. Cube root of 432: ∛432 ≈ 7.999. The cube root of 432 is not a whole number, so it is not a perfect cube.
3. Cube root of 36: ∛36 = 3. The cube root of 36 is a whole number, so it is a perfect cube.
4. Cube root of 250: ∛250 ≈ 6.299. The cube root of 250 is not a whole number, so it is not a perfect cube.
5. Cube root of 216: ∛216 = 6. The cube root of 216 is a whole number, so it is a perfect cube.
6. Cube root of 625: ∛625 = 5. The cube root of 625 is a whole number, so it is a perfect cube.
7. Cube root of 25: ∛25 = 2. The cube root of 25 is not a whole number, so it is not a perfect cube.
Based on this analysis, the numbers 36, 216, and 625 are perfect cubes.