Cubes and Cube Roots

JCERT · Class 8 · Chapter 3 · Cubes and Cube Roots. Syllabus-aligned topic notes and teaching examples, not a complete textbook answer key.

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Why This Chapter Matters

JCERT · Class 8 · Chapter 3 · Cubes and Cube Roots. Syllabus-aligned topic notes and teaching examples, not a complete textbook answer key.

Before You Begin (Prerequisites)

Revise the relevant ideas from the previous grade.

What You Will Learn (Core Objectives)

A cube a³ multiplies a three times. Group prime factors in triples to find cube roots. A negative number has a negative cube and a negative real cube root. Apply the method to decimals and rational numbers.

Chapter Roadmap & Progression

1 Syllabus, textbook and notes alignm...

2 Concept and method

3 Check and common pitfall

Complete Concept Guide (100% Curriculum Coverage)

Syllabus, textbook and notes alignment

JCERT · Regular schools (Non-SOE) · Class 8 · Chapter 3 — Cubes and Cube Roots
Official syllabus pages 63–77. Official syllabus · Prescribed Hindi book (17 chapters).

These topic notes and teaching examples are not a complete answer key to every textbook exercise. English notes use this same JCERT chapter order; a matching English textbook PDF has not been verified.

Official Hindi PDF for this exact chapter

Concept and method

A cube a³ multiplies a three times. Group prime factors in triples to find cube roots. A negative number has a negative cube and a negative real cube root. Apply the method to decimals and rational numbers.

Check and common pitfall

Check (−12)³=−1728 and (3/4)³=27/64.

Key Formulas, Identities & Theorems

Key relationships

∛(a/b)=∛a/∛b, b≠0; 1729=1³+12³=9³+10³

Observe formula conditions and units.

Conceptual Solved Examples & Case Studies

Example 1

Find the cube roots of −1728 and 27/64.

Step-by-Step Solution:

∛(−1728)=−12; ∛(27/64)=3/4

Check (−12)³=−1728 and (3/4)³=27/64.

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