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Syllabus
Squares and Square Roots — Syllabus
Gujarat Board · Class 8 · Mathematics
What Squares and Square Roots covers in Gujarat Board Class 8 Mathematics: 4 topics, for the 2026-27 session. Topics include Square Numbers and Perfect.
45 questions6 formulas & key relations5 concepts
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4 Topics · Gujarat Board Class 8 Mathematics · 2026-27
Topics in Squares and Square Roots
1
Square Numbers and Perfect Squares
- A square number (or perfect square) is a number that can be expressed as n² where n is a natural number. Examples: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100.
- The first 20 perfect squares are: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400.
- If a number cannot be expressed as n² for any natural number n, it is NOT a perfect square.
2
Properties of Square Numbers
- UNITS DIGIT RULE: A perfect square can only end in 0, 1, 4, 5, 6, or 9. It can NEVER end in 2, 3, 7, or 8.
- UNITS DIGIT PATTERN: If a number ends in 1 or 9, its square ends in 1. If it ends in 2 or 8, its square ends in 4. If it ends in 3 or 7, its square ends in 9. If it ends in 4 or 6, its square ends in
- TRAILING ZEROS: A perfect square always has an even number of zeros at its end. For example, 100 (2 zeros), 10000 (4 zeros). A number with an odd number of zeros (like 1000) is NOT a perfect square.
3
Finding the Square of a Number
- For any two-digit number, split it as (a + b) where a is a multiple of 10 and b is the units digit, then use (a+b)² = a² + 2ab + b².
- Special shortcut for numbers ending in 5: If a number ends in 5, its square = (preceding digits × next number) followed by 25. Example: 65² = (6×7) hundreds + 25 = 4225.
- Product of two consecutive odd/even numbers: (a-1)(a+1) = a² - 1. Example: 19 × 21 = 20² - 1 = 399.
4
Pythagorean Triplets
- A Pythagorean triplet is a set of three natural numbers (a, b, c) such that a² + b² = c², where c is the largest.
- Common Pythagorean triplets to memorise: (3,4,5), (5,12,13), (8,15,17), (7,24,25), (6,8,10), (9,40,41).
- General formula: For any natural number m > 1, the triplet is (2m, m²-1, m²+1).
Key Concepts
A square number is a naturalSquare numbers have distinct characteristicsSeveral interesting patterns exist in squareUsing algebraic identitiesA Pythagorean triplet consists of three
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Start This ChapterFrequently Asked Questions
What are the important topics in Squares and Square Roots for Gujarat Board Class 8 Mathematics?
Key topics in Squares and Square Roots include Square Numbers and Perfect Squares, Properties of Square Numbers, Finding the Square of a Number, Pythagorean Triplets. Study these first, then practise questions on each for Class 8 exams.
How should I revise Squares and Square Roots for Class 8 exams?
Learn the core ideas first, then work through the 45 practice questions on Squares and Square Roots. Revise definitions regularly and use flashcards for quick recall before the exam.
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Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.
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