Squares and Square Roots — Formula Sheet
Gujarat Board · Class 8 · Mathematics
6 formulas from Squares and Square Roots (Gujarat Board Class 8 Mathematics) on one page, grouped by topic. Includes Special shortcut for numbers, Product.
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Formulas and Key Relations
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.
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.
Key relations
For example, to find 23²
Express 23 = 20 + 3, then use (a + b)² = a² + 2ab + b².
A Pythagorean triplet consists of three natural numbers a, b, and c such that a² + b² = c².
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Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.
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