Cube roots in two seconds

From the sub-sutra Vilokanam, By mere observation, in Bharati Krishna Tirtha's 1965 book Vedic Mathematics. Deep dive into the sub-sutra

Try it with your numbers

Perfect cube

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When to use it

Cube roots of perfect cubes up to 970299 (roots up to 99).

The idea

Each last digit of a cube comes from exactly one last digit of the root. The thousands part tells the tens digit.

Worked example: ∛74088

1. …8 → 2Last digit 8 → root ends in 2 (2 and 8 swap, 3 and 7 swap, the rest stay).
2. 74 → 4Drop the last three digits: 74. Biggest cube not above it: 4³ = 64. Tens digit 4.
3. ∛74,088 = 42So the cube root of 74,088 is 42.

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.