Square numbers near a base

From the sutra Yāvadūnam, Whatever the extent of its deficiency, in Bharati Krishna Tirtha's 1965 book Vedic Mathematics. Deep dive into the sutra

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Number near a base

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When to use it

Squaring numbers near 10, 100 or 1000: 97², 104², 1012².

The idea

Find how far the number is from the base. Move that far again (left part), then square the distance (right part).

Worked example: 97²

1. 97 −397 is short of 100 by 3.
2. 94 | Go down by 3 again: 97 − 3 = 94.
3. 94 | 09Square the distance: 3² = 9, written with 2 digits.
4. 9409So 97² = 9409.

Practice this trick

All 15 speed tricks, each with its calculator. The speed tricks use sutras from Bharati Krishna Tirtha's 1965 book Vedic Mathematics; the lessons, problems and pictures here are our own.