Cubes and cube roots by prime factorisation: Class 8 practice
A perfect cube's prime factors group into triples. Read the method, follow the three worked examples, then try the six questions.
What you should know first
- Prime factorisation
- Cubes up to 20³
The idea behind cubes and cube roots by prime factorisation
A perfect cube's prime factors group into triples. Take one prime from each triple to find the cube root. If some primes are left over, multiply (or divide) by them to make a perfect cube.
Step-by-step method
- Prime factorise the number.
- Group equal primes in threes.
- Cube root = product of one prime per group.
- Leftover primes tell you what to multiply or divide by.
Worked example 1 (Basic)
Find the cube root of 1728 by prime factorisation.
- 1728 = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3
- Group in triples → 12
- Answer: 12
Worked example 2 (Standard)
Find the cube root of 9261 by prime factorisation.
- 9261 = 3 × 3 × 3 × 7 × 7 × 7
- Group in triples → 21
- Answer: 21
Worked example 3 (Challenge)
Find the smallest number by which 81000 must be divided to give a perfect cube, and the cube root of the result.
- 81000 = 2 × 2 × 2 × 3 × 3 × 3 × 3 × 5 × 5 × 5
- Divide by 3: 27000 = 30³
- Answer: Divide by 3; cube root 30
Common mistakes and misconceptions
- Grouping in pairs
- Forgetting leftover primes
Practice questions
- (Basic) Find the cube root of 125 by prime factorisation.
- (Basic) Find the cube root of 1000 by prime factorisation.
- (Standard) Find the cube root of 21952 by prime factorisation.
- (Standard) Find the cube root of 6859 by prime factorisation.
- (Challenge) Find the smallest number by which 27648 must be divided to give a perfect cube, and the cube root of the result.
- (Challenge) Find the smallest number by which 2000 must be divided to give a perfect cube, and the cube root of the result.
Answer key with full working
- Q1: 125 = 5 × 5 × 5 → Group in triples → 5 → Answer: 5
- Q2: 1000 = 2 × 2 × 2 × 5 × 5 × 5 → Group in triples → 10 → Answer: 10
- Q3: 21952 = 2 × 2 × 2 × 2 × 2 × 2 × 7 × 7 × 7 → Group in triples → 28 → Answer: 28
- Q4: 6859 = 19 × 19 × 19 → Group in triples → 19 → Answer: 19
- Q5: 27648 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 → Divide by 2: 13824 = 24³ → Answer: Divide by 2; cube root 24
- Q6: 2000 = 2 × 2 × 2 × 2 × 5 × 5 × 5 → Divide by 2: 1000 = 10³ → Answer: Divide by 2; cube root 10
Syllabus note
This skill is listed under "Cubes and Cube Roots" for Class 8 in the NCERT/CBSE books. ICSE, IGCSE, IB and state boards may teach it in a different chapter or year.
Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.
Related practice and notes
Frequently asked questions
Which chapter is cubes and cube roots by prime factorisation in?
"Cubes and Cube Roots", Class 8 Maths (NCERT/CBSE). Other boards may place it differently.
How were the answers checked?
Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.