2. Finding the Square of a Number

(a) Using Multiplication

The simplest way to find the square of a number is to multiply it by itself.
Example:

• 6² = 6 × 6 = 36

• 12² = 12 × 12 = 144

(b) Using the Formula for Expansion

For numbers close to a base value, we can use:
(a + b)² = a² + 2ab + b²
Example: Find 42²

• 42 = (40 + 2)

• 42² = 40² + 2(40 × 2) + 2²

• 1600 + 160 + 4 = 1764

(c) Special Case for Numbers Ending in 5

For numbers ending in 5, use:
(n5)² = n × (n+1) followed by 25
Example: Find 35²

• 3 × 4 = 12

• Attach 25 → 1225

(d) Using the Difference of Squares Formula

a² – b² = (a – b)(a + b)
Example: Find 49²

• 49² = (50 – 1)² = 50² – 2(50 × 1) + 1²

• 2500 – 100 + 1 = 2401