All About Numbers
Perfect Cubes – Numbers with Whole Cube Roots
A perfect cube is a whole number whose cube root is also a whole number – 1, 8, 27, 64, 125, and so on, exactly the cube numbers covered earlier in this section, now viewed from the opposite direction. Just as spotting perfect squares helps with square roots, recognising perfect cubes on sight makes cube-root calculations and radical simplification far faster.
Checking for a Perfect Cube
A number is a perfect cube if some whole number, cubed, produces it exactly.
Is 216 a perfect cube?
6 × 6 × 6 = 216, so 216 is a perfect cube.
Finding the Next Perfect Cube
What is the next perfect cube after 125?
125 = 5³. The next perfect cube is 6³ = 216.
Real-Life Application
- Packing and storage: checking whether a volume corresponds to a whole-number cube arrangement.
- Simplifying radicals: spotting perfect cube factors when simplifying cube roots.
- 3D design: designing cube-shaped containers with whole-number dimensions.
Key Takeaways
- A perfect cube has an exact whole-number cube root.
- The perfect cubes are 1, 8, 27, 64, 125, 216, 343…
- Estimating square roots, covered next, handles numbers that aren't perfect squares (or cubes).
Practice: Perfect Cubes
Is It a Perfect Cube?