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.
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