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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).

e.g.98298^2

Watch it solved

Live Demo
Working Base
100
number
98
-2
deficiency
1

Choose the base

98 is near 100. deficiency 2.

1 / 5

⚡ Speed Advantage

Vedic
2 steps
Traditional
8 steps

4× faster with Vedic Mathematics

When you’ll actually hit this

Real moments — exams, homework, competitions — where this shortcut earns its keep.

Homework

A mensuration question wants 103² for a 103 m × 103 m field.

becomes1032103^2

Surplus +3: left 103+3 = 106, right 3² = 09 → 10609.

Competition

Rapid-fire quiz: 997² flashes up and you have a few seconds.

becomes9972997^2

Deficiency −3: left 997−3 = 994, right 3² = 009 → 994009.

Mental check

A quick area check: a 98 mm square tile.

becomes98298^2

Deficiency −2: left 96, right 2² = 04 → 9604.

Exam crunch

A surplus over 100 with a carry — 112² in a timed set.

becomes1122112^2

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: 982=98×9898^2 = 98\times 98 via long multiplication. Yaavadunam: deficiency 2, left=982=9698-2=96, right=22=0496042^2=04 \to 9604 (2 steps).

2 mental steps vs 8+ for squaring numbers near a base.

Use when

  • Squaring a number close to 10, 100, 1000, etc.

Avoid when

  • Numbers ending in 5 (use Ekadhikena), numbers far from base

Master it