Squares and Square Roots

JCERT · Class 8 · Chapter 2 · Squares and Square 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 2 · Squares and Square 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 square is a number multiplied by itself. Study square patterns, sums of consecutive odd numbers and Pythagorean triples. Find square roots by subtraction, prime factorisation or long division, including decimals and fractions.

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 2 — Squares and Square Roots
Official syllabus pages 34–62. 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 square is a number multiplied by itself. Study square patterns, sums of consecutive odd numbers and Pythagorean triples. Find square roots by subtraction, prime factorisation or long division, including decimals and fractions.

Check and common pitfall

Check 0.09²=0.0081. The principal square root of a positive number is positive.

Key Formulas, Identities & Theorems

Key relationships

(a+b)²=a²+2ab+b²; √(a/b)=√a/√b, a≥0,b>0

Observe formula conditions and units.

Conceptual Solved Examples & Case Studies

Example 1

Find √1225 and √0.0081.

Step-by-Step Solution:

1225=5²×7²; √1225=35; √0.0081=0.09

Check 0.09²=0.0081. The principal square root of a positive number is positive.

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