Technique explanation
For a number N near base B with deficiency d = N - B, the cube is calculated using the Yaavadunam method: N^3 = (N + 2d) | 3d^2 | d^3. Each part (except the leftmost) must contain as many digits as the base has zeros.
This method is best for numbers within 10% of the base. Standard fallback: Standard long multiplication or the algebraic expansion (B + d)³.
Worked examples
Example 1: 104 cubed
- Base: 100. Deficiency (d): +4.
- Left Part: 104 + 2(4) = 112.
- Middle Part: 3(4^2) = 48.
- Right Part: 4^3 = 64.
- Combine: 112 | 48 | 64 = 1124864.
- Check: 104 × 104 × 104 = 1,124,864.
Example 2: 96 cubed
- Base: 100. Deficiency (d): -4.
- Left Part: 96 + 2(-4) = 88.
- Middle Part: 3(-4)^2 = 48.
- Right Part: (-4)^3 = -64.
- Normalize: 88 | 48 | -64 = 884800 - 64 = 884736.
- Check: 96 × 96 × 96 = 884,736.
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