5-ல் முடியும் எண்களை இரட்டிப்பாக்கல்
Squaring Numbers Ending in 5
35² = 1225. 75² = 5625. Any number ending in 5 squared in two steps. Once you see the pattern, you will never forget it.
Let's Learn
What you will learn today
Square any number ending in 5 using the Ekadhikena sutra in two mental steps.
What does squaring mean?
35² means 35 × 35. 75² means 75 × 75. These look hard — but watch what happens when any number ends in 5.
Here is the Ekadhikena sutra: 'By one more than the one before.' For squaring numbers ending in 5, it works like this: take the digits before the 5, multiply by the next number up, then write 25 after it. Two steps. Done.
ஏகாதிகேன — முந்தையதை விட ஒன்று அதிகம்.
The rule
For any number of the form n5 (ending in 5):
- Take n (the digits before the 5)
- Multiply n by (n+1) — the next number after n
- Write 25 after the result
- That is your answer
📐 35² — step by step
35 ends in 5. The digit before 5 is 3.
- 1n = 3
- 2n × (n+1) = 3 × 4 = 12
- 3Append 25: 1225
- 435² = 1225. Verify: 35 × 35 = 35 × 30 + 35 × 5 = 1050 + 175 = 1225 ✓
📐 75² — step by step
n = 7.
- 17 × (7+1) = 7 × 8 = 56
- 2Append 25: 5625
- 375² = 5625 ✓
📐 105² — step by step
105 ends in 5. The digits before 5 are 10.
- 1n = 10
- 210 × (10+1) = 10 × 11 = 110
- 3Append 25: 11025
- 4105² = 11025 ✓
Why does this work?
Let the number be (10n + 5). Then: (10n+5)² = 100n² + 100n + 25 = 100n(n+1) + 25. The first part, 100n(n+1), is just n(n+1) with two zeros — i.e., n(n+1) followed by '00'. Then we add 25 — replacing the '00' with '25'. That is exactly what the rule does.
ஏன் வேலை செய்கிறது: (10n+5)² = 100n(n+1) + 25.
Try: 45²
n = 4. Calculate n(n+1), then append 25. What is 45²?
Challenge Round
Challenge: 95² and 115²
Apply the rule to both. The second one has a two-digit n — handle it carefully.
Ekadhikena rule for ×5-ending squares: n × (n+1) then append 25. Works for any number ending in 5, any size.
↪ Next: Multiplying numbers near 10 using the base method.
Key Points
முக்கிய குறிப்புகள்
- ✓Rule: n5² = n(n+1) followed by 25
- ✓Works for ANY number ending in 5 (25, 35, 75, 105, 115...)
- ✓Why: algebraic identity (10n+5)² = 100n(n+1) + 25
- ✓Two steps: multiply the leading digits × (leading digits + 1), append 25
Glossary
சொல் அகராதி
Ekadhikena
ஏகாதிகேன
Square
வர்க்கம்
Append
இணை
Leading digit
முன் இலக்கம்
Practice Activities
Quizவினாடி வினா
Answer each question to check your understanding.
What is 55²?
Fill in the Blanksஇடைவெளி நிரப்புக
Type the missing word and press Check or Enter.
Type the missing word and click Check.