Free demo · Vedic Maths · Lesson 3 · Sutra 1 · Ekadhikena Purvena

Square any number ending in 5

Sutra 1, Ekadhikena Purvena, means “by one more than the one before”. It squares numbers ending in 5 in two tiny steps.

352=?
3 × (3 + 1)3 × 4 = 12
|
always5 × 5 = 25

35² = 1225

  1. 1Take the digit before the 5 (3) and multiply it by one more (4): 3 × 4 = 12
  2. 2Write 25 on the right (5 × 5 = 25)
  3. ✓Join the parts: 1225
  4. +Bigger numbers too: 85² → 8 × 9 = 72 → 7225 · 105² → 10 × 11 = 110 → 11025

Your turn: 65² = ?

4225: 6 × 7 = 42 | 25

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  5. Enrol

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About this lesson

To square a number ending in 5, multiply the digits in front of the 5 by the next whole number, then write 25 at the end. For 35², 3 × 4 = 12, so 35² = 1225; for 85², 8 × 9 = 72, so 85² = 7225. This is the Vedic sutra Ekadhikena Purvena, “by one more than the one before”, and it works for numbers of any size, such as 105² = 11025.

Key points

  • Sutra 1: Ekadhikena Purvena
  • The two-part answer: n × (n + 1) | 25
  • Bigger numbers: 85² and 105²