Square numbers and cube numbers
n² = n × n; n³ = n × n × n. Memorise 1² to 15² and 1³ to 5³.
Square numbers: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225 (1² to 15²). Cube numbers: 1, 8, 27, 64, 125 (1³ to 5³). Recognising these instantly is a Year 7-8 fluency target.
Worked examples
7² = 49, 8² = 64, 9² = 81, 12² = 144.
2³ = 8, 3³ = 27, 4³ = 64, 5³ = 125.
√81 = 9, &cube;64 = 4. Inverse operations.
Frequently asked questions
Why bother memorising?
They appear in algebra (factorising x² - 49 = (x-7)(x+7)), Pythagoras and standard form. Quick recall saves time.
64 is both square and cube?
Yes — 8² and 4³. The smallest number that is both a square and a cube (other than 1).