Square and cube numbers
Recognise and use square numbers and cube numbers, and the notation for squared (²) and cubed (³)
What a learner can do afterwards
- Identify 49 as 7² and explain that 7 × 7 = 49
- Calculate 4³ = 64 and explain it means 4 × 4 × 4
- List the first ten square numbers
The lesson
A square number is what you get when you multiply a whole number by itself. We write it with a small raised 2, like 5². That little 2 means 5 × 5, so 5² = 25.
A cube number works the same way, but you multiply the number by itself three times instead of two. We write it with a small raised 3, like 4³. That means 4 × 4 × 4.
Let's work out 3³. The small 3 means multiply 3 by itself three times: 3 × 3 × 3. First, 3 × 3 = 9. Then 9 × 3 = 27. So 3³ = 27.
Squared numbers make a square shape, with the same number of rows and columns. Cubed numbers multiply the number three times, not two, so they grow much faster. 2² = 4, but 2³ = 8.
n² means n × n, and n³ means n × n × n. The tiny number tells you how many times to multiply.
Watch it
Where it sits
Learn first
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.