Vedic Math Secret
Squaring Numbers Ending in 5 (N5²)
Any integer ending in 5 has a square that always ends in 25. The leading digits are found by taking the tens digit N and multiplying it by the next integer (N + 1).
Mathematical Symmetry & Identity
$$(10N + 5)^2 = N(N + 1) \times 100 + 25$$
Visual Mental Pipeline
Step-by-Step Execution Rules
- 1 Take the tens digit N. Multiply N by (N + 1). Example for 65: Tens digit is 6. 6 × (6 + 1) = 6 × 7 = 42.
- 2 Append 25 to the product: Write 25 right after 42 → 4,225!
- 3 Proof: (10N + 5)² = 100N² + 100N + 25 = 100N(N+1) + 25.
Worked Examples & Thought Process
35²
Example 1
Step 1: 3 × 4 = 12
Step 2: Append 25 → 1225
= 1225
65²
Example 2
Step 1: 6 × 7 = 42
Step 2: Append 25 → 4225
= 4225
85²
Example 3
Step 1: 8 × 9 = 72
Step 2: Append 25 → 7225
= 7225
95²
Example 4
Step 1: 9 × 10 = 90
Step 2: Append 25 → 9025
= 9025
Ready to Hone Your Speed?
Put this shortcut into practice with 10 procedural, timed questions. Sharpen your reaction time and track your accuracy.