Worked examples
Squares around 100
104²
Surplus +4. Left = 104+4 = 108. Right = 4² = 16. → 10816.
104² = 10816
97²
Deficit -3. Left = 97-3 = 94. Right = 3² = 09. → 9409.
97² = 9409
112²
Surplus +12. Left = 112+12 = 124. Right = 12² = 144 → write 44, carry 1: 124+1 = 125. → 12544.
112² = 12544
Common mistakes
Keep the right block two digits
- Right block is (deviation)² padded to 2 digits for base 100: 3² = 09, not 9.
- Carry when the square exceeds 99 (as in 112²) into the left block.
- Add for surplus, subtract for deficit — the sign of the deviation decides.
Practice — your turn
Square each number
All are within 15 of 100.
- 104²
- 97²
- 108²
- 94²
- 112²
- 89²
- 103²
- 96²
- 111²
- 98²
Answer key: 104² = 10816 • 97² = 9409 • 108² = 11664 • 94² = 8836 • 112² = 12544 • 89² = 7921 • 103² = 10609 • 96² = 9216 • 111² = 12321 • 98² = 9604
More questions
Good to know
What if the number is far from 100?
The method still works but the right-hand square gets large and needs carrying. For numbers far from any base, crosswise squaring is usually cleaner.
Can I use base 50 or 200?
Yes, with a small adjustment (a multiplier for the left part). Start with base 100 until the core idea is automatic.
Vedic Maths — Veda Topper
Square Numbers Near a Base (Yavadunam)
When a number sits close to 100 — like 97, 92 or 106 — the sutra Yavadunam ("whatever the deficiency") squares it instantly. Adjust by the deficiency, then tack on the square of the deficiency.
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The rule (just below 100)
- Find the deficiency: how far the number is below 100.
- Left part = number − deficiency.
- Right part = deficiency squared (as 2 digits).
Example 1 — 97²
Deficiency: 100 − 97 = 3
Left: 97 − 3 = 94
Right: 3² = 09
Join: 94 | 09
97² = 9409
Example 2 — 92²
Deficiency: 8
Left: 92 − 8 = 84
Right: 8² = 64
Join: 84 | 64
92² = 8464
Example 3 (carry) — 88²
Deficiency: 12
Left: 88 − 12 = 76
Right: 12² = 144 → keep 44, carry 1
76 + 1 = 77
88² = 7744
Just above 100
Example 4 — 106²
Surplus: 6
Left: 106 + 6 = 112
Right: 6² = 36
Join: 112 | 36
106² = 11236
Why it works
(100 − d)² = 100(100 − 2d) + d² = 100(number − d) + d² — exactly the "subtract the deficiency, then square it" rule.
Practice (answers below):
1) 96² 2) 98² 3) 94² 4) 103² 5) 108²
Answers: 1) 9216 2) 9604 3) 8836 4) 10609 5) 11664
1) 96² 2) 98² 3) 94² 4) 103² 5) 108²
Answers: 1) 9216 2) 9604 3) 8836 4) 10609 5) 11664
More Vedic Maths tricks
← Vedic Maths home Multiply by 11 in one lineSquare numbers ending in 5Base multiplication (Nikhilam)Vertically & crosswiseInstant division by 9Subtraction: all from 9All 16 Sutras & 13 sub-sutras
Frequently asked questions
How do you square a number near 100 in Vedic Maths?
Subtract the deficiency from the number for the left part, and write the square of the deficiency as the right part. For 97: 97−3 = 94 and 3² = 09 → 9409.
Which sutra squares numbers near a base?
Yavadunam — "whatever the extent of its deficiency." It works near any base such as 100 or 1000.
Does Yavadunam work above the base?
Yes. Add the surplus instead of subtracting the deficiency, then append its square. 106² = 11236.
Learn all of this live. Veda Topper runs online Vedic Maths classes for kids and adults, worldwide. Book a free demo class → · WhatsApp us →