Cubes and Cube Roots
Class 8 · Mathematics
4 ideas in Class 8 Mathematics, explained in plain words, with games and quizzes to practise.
Cube Numbers
Part of: Cubes
A cube number is what you get when a number is multiplied by itself three times, like 4 × 4 × 4 = 64. It is called a cube because a cube with side 4 units is made of 64 unit cubes. Cubes of even numbers are even and cubes of odd numbers are odd.
Why it matters. Cubes link number, geometry and volume. Knowing the first ten cubes helps with volume problems and with spotting patterns in larger numbers.
Try it in two minutes
- Build a 2 by 2 by 2 cube with small blocks or sugar cubes. Count the blocks.
- Ask how many blocks a 3 by 3 by 3 cube needs.
- Write the cubes of 1 to 5 together and check the units digits.
Try at home. Ask your child to build or draw a cube of side 3 and find how many small cubes it holds.
Patterns with Cubes
Part of: Cubes
Cubes have patterns too. The cube n³ can be written as the sum of n consecutive odd numbers: 3³ = 7 + 9 + 11 = 27. The difference between two neighbouring cubes follows the rule n³ - (n - 1)³ = 1 + 3 × n × (n - 1). The number 1729 is the smallest that is a sum of two cubes in two ways.
Why it matters. Looking for patterns trains children to predict and to check answers by a second method, which is the heart of maths thinking.
Try it in two minutes
- Ask your child to add 1, then 3 + 5, then 7 + 9 + 11. What do the totals look like?
- Ask: what could be the sum of the next 4 odd numbers?
- Check 3³ - 2³ with the pattern 1 + 3 × 3 × 2.
Try at home. Ask your child to find 6³ - 5³ by the pattern and also by cubing and subtracting.
Cubes and Prime Factors
Part of: Cubes
A perfect cube has its prime factors in triples. For example 216 = 2 × 2 × 2 × 3 × 3 × 3, so it is (2 × 3)³ = 6³. If one prime has no triple, we can multiply by the missing factors to make a cube, or divide to remove the leftover factors.
Why it matters. Prime factors show the hidden structure of a number. This idea reappears in algebra, in simplifying roots and in volume problems about stacking boxes into cubes.
Try it in two minutes
- Write 64 as a product of primes. Ask your child to circle groups of three.
- Do the same with 200 and see which prime is left over.
- Ask what to multiply 200 by so that all primes come in triples.
Try at home. Ask your child to find the smallest number to multiply 54 by to get a perfect cube.
Cube Roots
Part of: Cube roots
The cube root of a number is the number that, multiplied by itself three times, gives it. So the cube root of 27 is 3, written with a small 3 on the root sign. To find it for large numbers, break the number into prime factors, make groups of three equal factors, and take one from each group.
Why it matters. Cube roots are used when we know a volume and want the edge of a cube. They also strengthen the link between multiplication and its inverse.
Try it in two minutes
- Ask: a cube-shaped box holds 64 cubic cm. How long is its edge?
- Try 4 × 4 × 4 to check.
- Try 125 using prime factors 5 × 5 × 5.
Try at home. Ask your child to find the edge of a cube whose volume is 343 cubic cm.
What your child will practise
- Cube Numbers: Candy Quest (Flip and Match)
- Cube Numbers: Number Quest (Match It Up)
- Cube Roots: Ocean Puzzle (Clue Puzzle)
- Cubes and Prime Factors: Candy Quick Fire (Quick Fire)
- Patterns with Cubes: Lab Explorer Quest (Collect the Answer)
- Quiz: Cube Numbers (8 questions)
- Quiz: Cube Roots (8 questions)
- Quiz: Cubes and Prime Factors (8 questions)
- Quiz: Patterns with Cubes (8 questions)