Square numbers
Square a number sitting near 100 or 1000
Squaring 98 or 103 by long multiplication ignores how close they are to a round number.
Spot it when
The number is within ~15% of a power of 10 (98, 103, 997, 112).
Watch it solved
Choose the base
98 is near 100. deficiency 2.
⚡ Speed Advantage
4× faster with Vedic Mathematics
When you’ll actually hit this
Real moments — exams, homework, competitions — where this shortcut earns its keep.
A mensuration question wants 103² for a 103 m × 103 m field.
Surplus +3: left 103+3 = 106, right 3² = 09 → 10609.
Rapid-fire quiz: 997² flashes up and you have a few seconds.
Deficiency −3: left 997−3 = 994, right 3² = 009 → 994009.
A quick area check: a 98 mm square tile.
Deficiency −2: left 96, right 2² = 04 → 9604.
A surplus over 100 with a carry — 112² in a timed set.
Surplus +12: 112+12 = 124, 12² = 144; carry the extra hundred → 12544.
The method behind it
यावदूनम्
Yāvadūnaṃ
“Whatever the deficiency”
Square a number near a base: subtract (or add) the deficiency to get the left part, square the deficiency for the right part.
Conventional: via long multiplication. Yaavadunam: deficiency 2, left=, right= (2 steps).
Use when
- • Squaring a number close to 10, 100, 1000, etc.
Avoid when
- • Numbers ending in 5 (use Ekadhikena), numbers far from base