Square and cube numbers
Use integer powers and associated real roots (square, cube, and higher); recognise powers of 2, 3, 4, and 5; distinguish between exact representations of roots and their decimal approximations
What a learner can do afterwards
- Calculate squares, cubes, and higher integer powers of whole numbers
- Find square roots and cube roots of perfect squares and perfect cubes
- Recognise key powers (powers of 2 up to 2¹⁰, powers of 3 up to 3⁵, etc.) and distinguish exact roots from approximations
The lesson
A square number comes from multiplying a whole number by itself. We write this as n², which means n × n. For example, 4² = 4 × 4 = 16.
A cube number comes from multiplying a whole number by itself three times. We write this as n³, which means n × n × n. For example, 2³ = 2 × 2 × 2 = 8.
Priya wants to find 5² and 3³. She works out 5² = 5 × 5 = 25, and 3³ = 3 × 3 × 3 = 27. Squaring and cubing start the same way, but cubing multiplies by the number one more time.
Finding a square root or cube root undoes squaring or cubing. √25 = 5 exactly, because 5² = 25. But not every root is exact. √50 falls between 7 and 8, because 7² = 49 and 8² = 64, so we say it is close to 7 rather than exact.
Squaring multiplies a number by itself once, cubing multiplies it twice more, and roots undo both, though not every root comes out as a whole number.
Watch it
Where it sits
Learn first
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.