NCERT Class 8 Mathematics Mathematics: Chapter 6 — Cubes and Cube Roots
This chapter introduces the concept of cubes and cube roots, starting with an anecdote about the Hardy-Ramanujan number 1729. It explains that a perfect cube is a number obtained by multiplying a natural number by itself three times (e.g., 1=1³, 8=2³, 27=3³). The chapter provides tables to list cubes of numbers from 1 to 10 and 11 to 20, encouraging students to complete them. It also prompts observation about the parity of cubes (even cubes from even numbers, odd cubes from odd numbers). The text defines cubes in the context of solid figures and lays the groundwork for understanding cube roots and their properties, essential for CBSE Mathematics curriculum.
Quick info
| Board | CBSE / NCERT |
|---|---|
| Class | Class 8 |
| Subject | Mathematics |
| Book | Mathematics |
| Chapter | Chapter 6 — Cubes and Cube Roots |
| Language | English |
| PDF type | NCERT Textbook |
| Session | CBSE 2026 |
| Reading time | 3 minutes |
| Word count | 579 |
Learning outcomes
- Understand the definition of a perfect cube and cube number.
- Identify numbers that are perfect cubes.
- Calculate cubes of natural numbers.
- Observe patterns in the cubes of even and odd numbers.
- Recognize the Hardy-Ramanujan number as an example of sums of cubes.
Vocabulary
| Word | Meaning |
|---|---|
| Cube | A solid figure with all sides equal; or a number obtained by multiplying a number by itself three times. |
| Perfect cube | A number that can be expressed as the cube of an integer (e.g., 1, 8, 27). |
| Cube number | Same as a perfect cube. |
| Hardy-Ramanujan Number | The smallest number expressible as the sum of two cubes in two different ways (1729). |
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Practice questions
- What is a perfect cube? Answer: A perfect cube is a number that is the result of cubing an integer (multiplying it by itself three times).
- Is 64 a perfect cube? If yes, what is its cube root? Answer: Yes, 64 is a perfect cube because 4 × 4 × 4 = 64. Its cube root is 4.
- Find the cube of 5. Answer: The cube of 5 is 5 × 5 × 5 = 125.
- What can you say about the cube of an odd number? Answer: The cube of an odd number is always an odd number.
Frequently asked questions
What is the Hardy-Ramanujan number mentioned in the chapter?
The Hardy-Ramanujan number is 1729, the smallest number that can be expressed as the sum of two cubes in two different ways (1³ + 12³ and 9³ + 10³).
How is a perfect cube defined in mathematics?
A perfect cube is a number that is the result of multiplying an integer by itself three times. For example, 8 is a perfect cube because 2 × 2 × 2 = 8.
What are some examples of perfect cubes?
Examples of perfect cubes include 1 (1³), 8 (2³), 27 (3³), 64 (4³), and 125 (5³).
Are the cubes of even numbers always even?
Yes, the cubes of even numbers are always even. For example, 2³ = 8, 4³ = 64.
Are the cubes of odd numbers always odd?
Yes, the cubes of odd numbers are always odd. For example, 3³ = 27, 5³ = 125.
How many perfect cubes are there between 1 and 1000?
There are exactly ten perfect cubes between 1 and 1000: 1³, 2³, 3³, 4³, 5³, 6³, 7³, 8³, 9³, and 10³.
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Topics covered
NCERT Class 8 Mathematics — Mathematics — Chapter 6 — Cubes and Cube Roots. Verified by NCERT Help Editorial Team. Reviewed on 29 Jul 2026. Last updated 10 Aug 2026.