Round to the nearest thousand this time. The correction a is now three digits, so squaring it recurses one level deeper — and holding onto its square while you finish the rest of the calculation is exactly where the Major System earns its keep.
6382² = (6382+382)(6382−382) + 382²= 6764 × 6000 + 382²6764 × 6000 = 40 584 000 — hold onto "584" as a word (5=L, 8=V, 4=R → "lever")382² = (382−2)(382+2) + 2² = 380 × 384 + 4 = 145 92440 584 000 + 145 924 = 40 729 924
"lever" is a real word — the whole point of the Major System is picking a word that means something, not just any consonant string.
The live example below shows a simpler one-step version — round to the nearest ten instead of a thousand — which works for any digit count but skips the Major System step.
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Practice 4d²