Yāvadūnaṃ — Whatever the deficiency

यावदूनम् — Yaavadunam

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.

Why it works: For n near base B with deficiency d (n = B−d): n² = (B−d)² = B²−2Bd+d² = B(B−2d)+d² = B(n−d)+d². Left part = n−d = B−2d; right part = d². Above base: n = B+d → n² = B(n+d)+d².

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

Best for

• Squaring numbers near powers of 10

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Originally published at https://www.sutraflow.app/sutras/yaavadunam