Which number is a perfect cube? O 648 432 36 250 216 625 25
The number 216 can be expressed as a perfect cube because it is equal to 6 raised to the power of 3, or 6^3.
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.
To determine which number is a perfect cube, we need to find the numbers that can be expressed as the cube of an integer. Let's go through the given options:
1. 648 is not a perfect cube because it is divisible by 2 but not divisible by 3, so it cannot be expressed as the cube of an integer.
2. 432 is not a perfect cube because it is divisible by 2, but not divisible by 3, so it cannot be expressed as the cube of an integer.
3. 36 is a perfect cube because it can be expressed as 6 x 6 x 6, or 6^3.
4. 250 is not a perfect cube because it is not divisible by any cube number, such as 2^3, 3^3, 4^3, etc.
5. 216 is a perfect cube because it can be expressed as 6 x 6 x 6, or 6^3.
6. 625 is not a perfect cube because it is not divisible by any cube number.
7. 25 is not a perfect cube because it is not divisible by any cube number.
Therefore, the numbers 36 and 216 are perfect cubes.