Class 8 Mathematics – Cubes and Cube Roots
These notes are prepared by Veezna Group of Institutes for Class 8 students. The chapter Cubes and Cube Roots is explained in very simple language with step-by-step solved examples, so students can understand easily and prepare confidently for exams.
1. Cube Numbers
When a number is multiplied by itself three times, the result is called a cube number.
Examples:
- 2 × 2 × 2 = 8 → 2³ = 8
- 3 × 3 × 3 = 27 → 3³ = 27
- 5 × 5 × 5 = 125 → 5³ = 125
Here, 2, 3, 5 are bases and 3 is the power.
2. Cubes of Natural Numbers
Some cubes of natural numbers are given below:
- 1³ = 1
- 2³ = 8
- 3³ = 27
- 4³ = 64
- 5³ = 125
- 6³ = 216
3. Properties of Cube Numbers
- Cubes of even numbers are even.
- Cubes of odd numbers are odd.
- A cube number can end with 0, 1, 4, 5, 6, 8, or 9.
Solved Example:
Is 729 a cube number?
9³ = 729
Therefore, 729 is a cube number.
4. Cube Roots
The cube root of a number is the value which, when multiplied by itself three times, gives the original number.
Symbol: ∛
Examples:
- ∛8 = 2
- ∛27 = 3
- ∛125 = 5
5. Finding Cube Roots by Prime Factorisation
Steps:
- Write the number as a product of prime factors.
- Make groups of three equal factors.
- Take one factor from each group.
Solved Example:
Find ∛216
216 = 2 × 2 × 2 × 3 × 3 × 3
Groups: (2×2×2), (3×3×3)
∛216 = 2 × 3 = 6
6. Estimating Cube Roots
Sometimes we estimate cube roots by finding nearby perfect cubes.
Solved Example:
Estimate ∛150
5³ = 125 and 6³ = 216
150 lies between 125 and 216
So, ∛150 lies between 5 and 6
Important Exam-Oriented Questions
Very Short Answer
- Write the cube of 7.
- Find ∛64.
Short Answer
- Is 343 a cube number? Give reason.
- Find ∛512 by prime factorisation.
Long Answer
- Explain the method of finding cube roots by prime factorisation.
- Estimate the cube root of 200.
Key Points for Exams
- Cube means number multiplied three times by itself.
- Cube root reverses the cube.
- Always make groups of three while finding cube roots.
- Write steps clearly for full marks.
Prepared with care by Veezna Group of Institutes to support learning and exam preparation.
