Sūtra 10 of 16

Yāvadūnam

Whatever the deficiency

Squaring numbers near a power of 10.

When to use

Squaring numbers near 100, 1000, etc.

How it works

For N near base B with deficit d (so N = B − d): N² = (N − d) | d². Left part is N minus the deficit; right part is d² (padded).

Memory formula

Near base square: left = N ± deviation; right = deviation² padded to base digits.

Worked examples

Problem 1

97²

0/4

Problem 2

104²

0/4

Try it yourself

Try to solve, then reveal the steps one at a time.

easy

Compute 96²

medium

Compute 108²

Modern applications

Where this ancient technique still lives in today's world.

Coding

Squaring near a power of 2

When squaring numbers near 2^n, the deficit/surplus trick reduces a multiply to a shift + small multiply — an SIMD optimisation pattern.

Code in your favourite language

Square a number near a base by adjusting deviation twice.

Python

def yavadunam_square(n: int, base: int) -> int:
    d = n - base
    left = n + d
    right = d * d
    digits = len(str(base)) - 1
    return left * (10 ** digits) + right

print(yavadunam_square(96, 100))  # 9216

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