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
1 · Read
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.
More to read
Meaning of exponents
A square number comes from multiplying a whole number by itself. 7 x 7 = 49, so 49 is 7 squared, written 7 with a small 2. The first ten square numbers are 1, 4, 9, 16, 25, 36, 49, 64, 81 and 100. Learning them by heart makes spotting squares instant. Arrays of dots in equal rows and columns show why they are called square.
Exponents review
An exponent tells you how many times to multiply. 4 cubed, written 4 with a small 3, means 4 x 4 x 4 = 64. The small number is not a multiplier: 4 with a small 3 is 64, not 12. Say cubed for a small 3 and squared for a small 2. Reading exponents aloud keeps their meaning clear.
Exponents and order of operations FAQ
Squares and cubes follow the order of operations like everything else. Work out 9 squared plus 2 cubed as 81 + 8 = 89, doing the powers before the adding. A frequent error is mixing 4 cubed with 4 x 3. Since 4 x 4 x 4 = 64 and 4 x 3 = 12, only the repeated multiplication is right.
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2 · Watch
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Where it sits
17 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.