Skip to content
Learn Vedic Math

Square any two-digit number

From the sutra Ūrdhva Tiryagbhyām, Vertically and crosswise, used for squares, in Bharati Krishna Tirtha's 1965 book Vedic Mathematics. Deep dive into the sutra

Try it with your numbers

When to use it

Squaring any two-digit number, like 47² or 83².

The idea

For ab²: write a², then 2 × a × b in the middle, then b², and carry from right to left.

Worked example: 47²

  1. 16 | 56 | 49Digits 4 and 7. Left: 4² = 16. Middle: 2 × 4 × 7 = 56. Right: 7² = 49.
  2. 16 | 56 | 49Keep one digit in each of the middle and right spots and carry the rest leftwards.
  3. 2209So 47² = 2209.

Practice this trick

All 15 speed tricks, each with its calculator. The speed tricks use sutras from Bharati Krishna Tirtha's 1965 book Vedic Mathematics; the lessons, problems and pictures here are our own.