Page 15 - Revised Maths Wisdom Class - 6

Patterns in Mathematics 13

ILLUSTRATIONS

Example 1: Find the square numbers between 100 to 400.
Solution: We know that 100 = 10 × 10 and 400 = 20 × 20. Therefore, the square numbers between 100
and 400 are:
11 × 11 = 121; 12 × 12 = 144; 13 × 13 = 169; 14 × 14 = 196; 15 × 15 = 225;
16 × 16 = 256; 17 × 17 = 289; 18 × 18 = 324; 19 × 19 = 361

Example 2: In a series of square numbers, find the next three square numbers.
484, 529, 576, ________, ________, ________.

Solution: Since 484 = 22 × 22, 529 = 23 × 23, 576 = 24 × 24
Hence, the next three square numbers are:

25 × 25 = 625, 26 × 26 = 676, 27 × 27 = 729
Example 3: Represent the following triangular or square numbers geometrically.

(a) 4 (b) 6 (c) 10 (d) 16 (e) 21 (f) 36
2

Solution: (a) Since 4 = 2 × 2 hence, it is a square number. It can be represented as 4 2

(b) Since 6 is a triangular number, hence it is represented as

(c) 10 is a triangular number, so it is represented as

(d) 16 = 4 × 4 can be represented as

(e) 21 is a triangular number, hence can be represented as