यावदूनम्
Yāvadūnaṃ
"Whatever the deficiency"
What this sutra solves
Square a number that sits near 100 or 1000 with almost no arithmetic.
A square tile is 98 mm on each side and you need its area.
Deficiency −2: 96 | 04 → 9604 sq mm.
A 103 m × 103 m field — area?
Surplus +3: 106 | 09 → 10609 sq m.
Choose the base
98 is near 100. deficiency 2.
⚡ Speed Advantage
4× faster with Vedic Mathematics
Best for
- • Squaring numbers near powers of 10
Use when
- • Squaring a number close to 10, 100, 1000, etc.
Avoid when
- • Numbers ending in 5 (use Ekadhikena), numbers far from base
Intuition
Square a number near a base: subtract (or add) the deficiency to get the left part, square the deficiency for the right part.
Story Mode
The Deficit Squared
How far are you from 100? That distance — your deficiency — is the key. Reduce the number by that same deficiency for the left, square the deficiency for the right. The base 100 acts like a scaffold that the final answer hangs from.
Vedic vs conventional
Conventional: via long multiplication. Yaavadunam: deficiency 2, left=, right= (2 steps).
Applications
Squaring numbers near a base
Any number within ~15% of a power of 10 squares in 2 steps.
Common Mistakes to Avoid
Padding the right part to match base digit count
Wrong approach
Correct approach
Why this happens
💡 Same error as Nikhilam — forgetting to pad.
Why It Works
Let the number be below the base:
Square it:
Factor by the base:
The left part is n minus the deficiency; the right part is the square of the deficiency, padded to the base width.
For n near base B with deficiency d (): ² = ()+()+d². Left part = ; right part = d². Above base: ()+d².