How do you find the cube root of a perfect cube (up to 6 digits) by inspection, e.g. ∛185193?

The cube's last digit fixes the root's last digit; the leading group fixes the tens digit.

Two facts to know: cubes 1³–9³, and the units-digit map (0→0, 1→1, 2→8, 3→7, 4→4, 5→5, 6→6, 7→3, 8→2, 9→9 — only 2↔8 and 3↔7 swap):

• ∛185193 → split 185 | 193. Last digit 3 → root ends in 7. Leading 185: largest cube ≤ 185 is 125 = 5³ → tens digit 5. → 57.

Check: 57³ = 185193. ✓ (Exact cubes only; for non-cubes, estimate instead.)