Mathematics · Class 8
Cubes and Cube Roots
Perfect cubes, cube roots, and identifying cube numbers.
4 sections15–25 min read6 MCQs · 2 examples
Chapter Overview
Cube numbers are n³. Find cube roots by prime factorisation — essential for volume problems involving cubes and cuboids.
Perfect Cubes
- 1, 8, 27, 64, 125, ...
- n³ = n × n × n
- Negative numbers can be perfect cubes: (−2)³ = −8
Cube Root
Definition
∛a = b if b³ = a
Factorisation
Group factors in triplets
Properties
Unit digit patterns for cubes repeat. Cube root of negative number is negative.
Solved Examples
Step-by-step solutions — read each step before checking the final answer.
Example 1: Cube Root
Find ∛216.
- 1216 = 6³
- 2Or 2³×3³
Answer
6
Example 2: Volume
Cube volume 343 cm³. Find edge.
- 1Edge = ∛343
- 27³ = 343
Answer
7 cm
Key Points to Remember
- ✓ ∛(a³) = a
- ✓ Cube of negative is negative
- ✓ Volume of cube = edge³
Exam Tips
- • Prime factorise and form triplets
- • Check by cubing answer
Practice MCQs — Cubes and Cube Roots
Test your understanding with topic-wise multiple choice questions. Explanations appear after each answer.
Question 1 of 6Score: 0/0
Cube of 4 is: