Cube Numbers and Roots
A cube is n×n×n; the cube root undoes it.
Key idea
A cube is n×n×n; the cube root undoes it.
In depth
A cube number is n × n × n, the volume of an n-sided cube. The cube root reverses it: ∛27 = 3. Unlike square roots, cube roots of negatives are real: ∛(−8) = −2.
Worked example
4³ = 64, so ∛64 = 4.
Formula
Real-world uses
- Working out the edge of a cube-shaped tank from its volume
- Comparing sizes of 3D boxes
Common mistake
Mixing up squaring and cubing: 3² = 9 but 3³ = 27.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Cube Numbers and Roots?
A cube is n×n×n; the cube root undoes it. It is a topic at the intermediate level in Arithmetic & Number Sense.
What is the formula for Cube Numbers and Roots?
The key formula is ∛(n³) = n.
Where is Cube Numbers and Roots used in real life?
Real-world examples: Working out the edge of a cube-shaped tank from its volume; Comparing sizes of 3D boxes.
What should I learn before Cube Numbers and Roots?
Make sure you are comfortable with Square Numbers and Roots, the previous topic in Arithmetic & Number Sense.
What is a common mistake with Cube Numbers and Roots?
Mixing up squaring and cubing: 3² = 9 but 3³ = 27.
How can I practise Cube Numbers and Roots?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Cube Numbers and Roots?
Move on to Negative Numbers next.
Related intermediate topics in Arithmetic & Number Sense
- Long Multiplication – Multiply by each digit of the multiplier, shift by place value, then add partial products.
- Long Division – Divide, multiply, subtract and bring down repeatedly to get the quotient.
- Factors and Multiples – Factors divide a number exactly; multiples are its products with whole numbers.
- Divisibility Rules – Quick tests: by 2 last digit even, by 3 digit-sum divisible by 3, by 5 ends 0/5, by 9 digit-sum divisible by 9.
- Prime Numbers – A prime has exactly two positive divisors: 1 and itself.
- Composite Numbers – Numbers greater than 1 with more than two factors.