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Revision Notes
Squares and Square Roots — Revision Notes
Gujarat Board · Class 8 · Mathematics
Squares and Square Roots revision notes for Gujarat Board Class 8 Mathematics: 4 topics in quick points. Includes Square Numbers and Perfect Squares.
45 questions6 formulas & key relations5 concepts
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Key Topics to Revise
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).
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Full NotesKey Concepts
A square number is a naturalSquare numbers have distinct characteristicsSeveral interesting patterns exist in squareUsing algebraic identitiesA Pythagorean triplet consists of three
Frequently 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.
Sources & Official References
Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.
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