Module 3 · Number System
Chapter 41: Perfect Cubes
Number System
2 topics
What this chapter covers
The 2 topics below make up Perfect Cubes on the CAT. Click any topic to open its notes, examples and practice test.
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Formula Reference Sheet
This chapter
Cubes & cube roots
| Cube of n | n³ = n × n × n |
|---|---|
| Cube root | ∛(n³) = n |
| Perfect-cube test (prime factors) | every prime exponent is a multiple of 3 |
| Difference of cubes | a³ − b³ = (a − b)(a² + ab + b²) |
| Sum of cubes | a³ + b³ = (a + b)(a² − ab + b²) |
Sum-of-cubes identities
| Sum of first n cubes | 1³ + 2³ + … + n³ = [n(n+1)/2]² |
|---|---|
| Link to triangular number | 1³ + 2³ + … + n³ = (1 + 2 + … + n)² |
| Sum of first n cubes | = [Σn]² where Σn = n(n+1)/2 |
| Cube of a binomial | (a + b)³ = a³ + 3a²b + 3ab² + b³ |
| Identity (a+b+c=0) | a³ + b³ + c³ = 3abc |
CAT reference
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