Vedic Maths for Kids· Lesson 4 of 10
5-ல் முடியும் எண்களை இரட்டிப்பாக்கல்
Squaring Numbers Ending in 5
~10 min
35² = 1225. 75² = 5625. Any number ending in 5 squared in two steps. Once you see the pattern, you will never forget it.
By the end of this lesson you will be able to— இந்த பாடத்தின் இறுதியில்
- Square any number ending in 5 using the Ekadhikena method
- Apply the steps: multiply the leading digit(s) by the next number up, then append 25
- Verify answers using the long multiplication method
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.
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.
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
- ✓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
Speed Drill · விரைவு பயிற்சி
×5-Ending Squares Drill
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 or press Enter.