Vedic Maths Sutra 01 : Ekādhikena Pūrveṇa
Sūtra 1 of 16
एकाधिकेन पूर्वेण
Ekādhikena Pūrveṇa
“By one more than the previous one”
Meaning & Essence
This Sūtra means “By one more than the previous one”. It is one of the most elegant and frequently used techniques in Vedic Mathematics, especially for finding the square of any number ending with 5.
The method is extremely fast and can be performed mentally within seconds.
Mathematical Principle
Let the number ending with 5 be written as \( 10a + 5 \), where \( a \) is the digit(s) before 5.
\[
(10a + 5)^2 = 100 \times a(a+1) + 25
\]
In simple words:
- Take the digit(s) before 5 → this is \( a \)
- Multiply \( a \) by \( (a + 1) \)
- Write the result and simply append 25 at the end
Worked Examples
Example 1 → Find \( 65^2 \)
- Here \( a = 6 \)
- \( a + 1 = 7 \)
- \( 6 \times 7 = 42 \)
- Append 25
Answer: 4225
Example 2 → Find \( 75^2 \)
- \( a = 7 \)
- \( 7 \times 8 = 56 \)
- Append 25
Answer: 5625
Example 3 → Find \( 125^2 \)
- \( a = 12 \)
- \( 12 \times 13 = 156 \)
- Append 25
Answer: 15625
Interactive Demo – Square any number ending with 5
Please enter a valid number that ends with 5
When to Use This Sūtra
• Squaring any number that ends with 5
• Can also be extended to numbers ending with 25, 75 etc. with slight modifications
• Extremely useful for competitive exams and mental math practice