• Key Stage 2 • Maths
A square number is the answer when you multiply a whole number by itself. Pupils learn square numbers and cube numbers in Year 5. This guide lists the square numbers to 225 and the cube numbers to 1000, explains the notation and gives practice questions with answers.
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The Quick Answer
- A square number is a number multiplied by itself, such as 5 × 5 = 25.
- The square numbers to 100 are 1, 4, 9, 16, 25, 36, 49, 64, 81 and 100.
- A cube number is a number multiplied by itself three times, such as 2 × 2 × 2 = 8.
- Pupils learn square numbers, cube numbers and the notation ² and ³ in Year 5.
What Is a Square Number?
A square number is the result of multiplying a whole number by itself. It is called a square number because that many dots or counters can be arranged into a square. For example, 9 counters make a square with 3 rows of 3.
The small 2 is the notation for squared. 4² means 4 × 4, so 4² = 16.
Square Numbers List
| Calculation | Square number |
|---|---|
| 1² = 1 × 1 | 1 |
| 2² = 2 × 2 | 4 |
| 3² = 3 × 3 | 9 |
| 4² = 4 × 4 | 16 |
| 5² = 5 × 5 | 25 |
| 6² = 6 × 6 | 36 |
| 7² = 7 × 7 | 49 |
| 8² = 8 × 8 | 64 |
| 9² = 9 × 9 | 81 |
| 10² = 10 × 10 | 100 |
| 11² = 11 × 11 | 121 |
| 12² = 12 × 12 | 144 |
| 13² = 13 × 13 | 169 |
| 14² = 14 × 14 | 196 |
| 15² = 15 × 15 | 225 |
The first 12 square numbers all come from the times tables, so pupils who know their tables up to 12 × 12 already know them.
What Is a Cube Number?
A cube number is a whole number multiplied by itself three times. The small 3 is the notation for cubed: 3³ = 3 × 3 × 3 = 27. It is called a cube number because that many small cubes can be built into a larger cube.
| Calculation | Cube number |
|---|---|
| 1³ = 1 × 1 × 1 | 1 |
| 2³ = 2 × 2 × 2 | 8 |
| 3³ = 3 × 3 × 3 | 27 |
| 4³ = 4 × 4 × 4 | 64 |
| 5³ = 5 × 5 × 5 | 125 |
| 6³ = 6 × 6 × 6 | 216 |
| 7³ = 7 × 7 × 7 | 343 |
| 8³ = 8 × 8 × 8 | 512 |
| 9³ = 9 × 9 × 9 | 729 |
| 10³ = 10 × 10 × 10 | 1000 |
Patterns in Square Numbers
- Adding odd numbers: 1 + 3 = 4, 1 + 3 + 5 = 9 and 1 + 3 + 5 + 7 = 16. Adding the odd numbers in order always makes a square number.
- Last digits: square numbers only ever end in 0, 1, 4, 5, 6 or 9. A number ending in 2, 3, 7 or 8 cannot be a square number.
- Square and cube: 1, 64 and 729 are both square numbers and cube numbers. For example, 64 = 8² and 64 = 4³.
- Number of factors: square numbers have an odd number of factors. The factors of 16 are 1, 2, 4, 8 and 16.
Tip: a common mistake is to think 4² means 4 × 2. It means 4 × 4. Saying “4 squared is 4 lots of 4” helps pupils remember.
Square and Cube Numbers Practice Questions
- 7²
- 11²
- 3³
- 5³
- Which of these are square numbers? 36, 48, 64, 90
- 6² + 2³
- 10² − 4²
- Find two square numbers that add up to 13.
- Find a number between 10 and 100 that is both a square number and a cube number.
- 9² ÷ 3
- Which number multiplied by itself makes 144?
- Is 50 a square number? Explain how you know.
Show the answers
- 49
- 121
- 27
- 125
- 36 and 64
- 36 + 8 = 44
- 100 − 16 = 84
- 4 and 9
- 64 (8² and 4³)
- 81 ÷ 3 = 27
- 12
- No. 7² = 49 and 8² = 64, so 50 falls between two square numbers.
Square Numbers in KS2
The Year 5 national curriculum says pupils should recognise and use square numbers, cube numbers and the notation for squared (²) and cubed (³). They are part of the content that can be assessed in the KS2 maths tests. In Year 6, pupils use them in calculations with the order of operations. Square numbers also come up in area: a square with sides of 7 cm has an area of 7² = 49 cm². Try our Year 6 arithmetic questions for more practice.
Frequently Asked Questions
What are the square numbers up to 100?
1, 4, 9, 16, 25, 36, 49, 64, 81 and 100.
Is 1 a square number?
Yes. 1 × 1 = 1, so 1 is a square number. It is also a cube number.
What is the difference between a square number and a cube number?
A square number is a number multiplied by itself (5² = 25). A cube number is a number multiplied by itself three times (5³ = 125).
What year do children learn square numbers?
Square and cube numbers are part of the Year 5 national curriculum.
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Sources: Department for Education, National curriculum in England: mathematics programmes of study; Standards and Testing Agency, KS2 mathematics test framework. Practice questions written by Monster Learning.
