🧠 Introduction
Ever felt stuck calculating squares of numbers like 61² or 85² in your head? You’re not alone. But here’s the secret — numbers ending in certain digits follow magical patterns that make squaring them super easy!
In this blog, we’ll reveal easy, time-saving tricks to quickly square numbers ending with 1, 2, 4, 5, 6, 9, and 10 — no calculator needed!
✅ 1. Numbers Ending in 1
Trick:(x1)² = x × (x + 1) × 100 + 1
Example:
31²
→ 3 × 4 = 12
→ 12 × 100 = 1200
→ 1200 + 1 = 1201
✅ 2. Numbers Ending in 2
Trick:(x2)² = x × (x + 1) × 100 + 4
Example:
42²
→ 4 × 5 = 20
→ 20 × 100 = 2000
→ 2000 + 4 = 2004
✅ 3. Numbers Ending in 4
Trick:(x4)² = x × (x + 1) × 100 + 16
Example:
64²
→ 6 × 7 = 42
→ 42 × 100 = 4200
→ 4200 + 16 = 4216
✅ 4. Numbers Ending in 5
Trick:(x5)² = x × (x + 1) then add 25 at the end.
Example:
85²
→ 8 × 9 = 72
→ Final answer = 7225
✅ 5. Numbers Ending in 6
Trick:(x6)² = x × (x + 1) × 100 + 36
Example:
36²
→ 3 × 4 = 12
→ 12 × 100 = 1200
→ 1200 + 36 = 1236
✅ 6. Numbers Ending in 9
Trick:(x9)² = x × (x + 1) × 100 + 81
Example:
59²
→ 5 × 6 = 30
→ 30 × 100 = 3000
→ 3000 + 81 = 3081
✅ 7. Numbers Ending in 0 or 10
Trick 1:
If number ends in 0,(10x)² = 100 × (x²)
Example:
70² = 7² × 100 = 4900
Trick 2:
Use algebra:(a + b)² = a² + 2ab + b²
Example:
110² = (100 + 10)²
→ 10000 + 2000 + 100 = 12100
💡 Bonus Tip
Use identities for quick calculation:(a + b)² = a² + 2ab + b²(a – b)² = a² – 2ab + b²
These help when squaring numbers near 100, 50, etc.
🏁 Final Thoughts
Mathematics isn’t always about long formulas. It’s about spotting patterns and playing smart. With these tricks, squaring becomes faster, easier, and more fun — perfect for students, exam-takers, or math enthusiasts!
