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A perfect cube is a number that can be expressed as the cube of an integer. In other words, a number is a perfect cube if its cube root is an integer.
| Example | Rewrite as a Product | Perfect Cube? | Explanation |
|---|---|---|---|
| 125 | 5 * 5 * 5=5^3 | Yes ✓ | 5 is an integer. |
| 166.375 | 5.5 * 5.5 * 5.5 = 5.5^3 | No * | 5.5 is not an integer. |
| 64 | 4 * 4 * 4=4^3 | Yes ✓ | 4 is an integer. |
| 270 | 3sqrt(10) * 3sqrt(10) * 3sqrt(10) = (3sqrt(10))^3 | No * | 3sqrt(10) is not an integer. |
Similarly, if a variable has an exponent that is a multiple of 3, it is still considered a perfect cube. This is because this condition guarantees that the variable can be rewritten as the product of three identical powers with integer exponents. y^3 & ⇔ y * y * y x^6 & ⇔ x^2 * x^2 * x^2