Squares_Class8_DAV based on squares and perfect squares and patterns

Squares on class8

1. Squares Class 8 Mathematics (CBSE/DAV) Prepared by: [Your Name] Topic: Squares and Square Numbers

2. Learning Objectives • Understand the concept of square numbers • Learn properties of perfect squares • Identify patterns in squares • Learn to find square numbers using formulas

3. Introduction to Squares A square number is the product of a number multiplied by itself. Example: 2 × 2 = 4, 3 × 3 = 9 Hence, 4 and 9 are perfect squares.

4. List of First 10 Squares 1² = 1 2² = 4 3² = 9 4² = 16 5² = 25 6² = 36 7² = 49 8² = 64 9² = 81 10² = 100

5. Properties of Square Numbers • The square of an even number is even. • The square of an odd number is odd. • A number ending in 2, 3, 7, or 8 cannot be a perfect square. • Squares of numbers ending in 5 always end in 25.

6. Patterns in Squares • Sum of first n odd numbers = n² Example: 1 + 3 + 5 = 9 = 3² • Difference between consecutive squares increases by 2 each time.

7. Square of a Number Ending in 5 If a number ends with 5, its square always ends in 25. Example: 35² = (3 × 4) and write 25 → 1225 45² = (4 × 5) and write 25 → 2025

8. Finding Squares Using Algebraic Identities (a + b)² = a² + 2ab + b² Example: 12² = (10 + 2)² = 100 + 40 + 4 = 144

9. Square Root and Perfect Squares If 9 is a perfect square, √9 = 3. Perfect squares have whole number square roots. Non-perfect squares have non-terminating, non-repeating roots.

10. Real-Life Applications of Squares • Area of square = side² • Designing tiles, fields, plots • Used in Pythagoras theorem (a² + b² = c²)

11. Thank You Reflect: What patterns can you notice in square numbers? Prepare a chart of 1 to 20 squares as homework.