Magic of Squares Ending with 5

Learn to calculate squares of numbers ending with 5 in seconds!

The Amazing Trick

n5²=n × (n+1)then append25

Step-by-Step:

  1. Remove the 5 from the number (let's call this n)
  2. Multiply n by (n + 1)
  3. Append 25 to the result

Examples

Example 1: 15²

n = 1 (remove the 5)

1 × (1 + 1) = 1 × 2 = 2

Append 25 → 225

∴ 15² = 225

Example 2: 45²

n = 4 (remove the 5)

4 × (4 + 1) = 4 × 5 = 20

Append 25 → 2025

∴ 45² = 2025

Example 3: 105²

n = 10 (remove the 5)

10 × (10 + 1) = 10 × 11 = 110

Append 25 → 11025

∴ 105² = 11,025

Why This Works

This trick works because of algebraic expansion:

(10n + 5)² = 100n² + 100n + 25

= 100n(n + 1) + 25

The pattern holds true for any number ending with 5!

Practice Now

Calculate: ²

Score: 0 / 0

Accuracy: 0%

Pro Tips

🚀 Speed Tip

For larger numbers, multiply the prefix mentally before appending 25.

🎯 Verification

Always ends with 25. If your answer doesn't end with 25, it's wrong!

💡 Pattern Recognition

Notice that 25²=625, 35²=1225, 45²=2025 - the pattern continues!