Page 189 - Math Skill - 5

Pattern, Net and Symmetry 187

Let’s Attempt

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

2

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

(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

Exercise 15.1

1. Complete the following patterns.

(a) 1 + 3 = 4
1 + 3 + 5 = 9
1 + 3 + 5 + 7 = 16
1 + 3 + 5 + 7 + 9 =

+ + + + + =