SarwaSamadhan

Cube root of a perfect cube in one look

पूर्ण घन का घनमूल एक नज़र में

For a perfect cube up to 6 digits, the last digit fixes the unit digit of the root and the leading digits fix the tens digit — no division needed.

अंतिम अंक से घनमूल का इकाई अंक, और शुरू के अंकों से दहाई का अंक — बिना भाग दिए।

Learn the cubes 1 to 10

1, 8, 27, 64, 125, 216, 343, 512, 729, 1000. Each ends in a different digit, so the last digit of a cube points to exactly one root digit:

  1. 1 → 1, 4 → 4, 5 → 5, 6 → 6, 9 → 9, 0 → 0 (same digit)
  2. 2 ↔ 8 and 3 ↔ 7 (they swap): a cube ending in 2 has a root ending in 8, ending in 8 → root ends in 2, ending in 3 → 7, ending in 7 → 3

The method

  1. Look at the last digit of the number → unit digit of the root.
  2. Strike off the last three digits. For the number left, find the largest n with n³ ≤ it → tens digit.
Example ∛110592
Ends in 2 → 8. Left part 110: 4³ = 64 ≤ 110 < 125 → 4 → 48
Example ∛857375
Ends in 5 → 5. Left part 857: 9³ = 729 ≤ 857 → 95
Example ∛175616
Ends in 6 → 6. Left part 175: 5³ = 125 → 56

Try it yourself · अभ्यास

  1. ∛274625 = ?
    Show answer

    Ends 5 → 5; 274: 6³ = 216 → 65

  2. ∛941192 = ?
    Show answer

    Ends 2 → 8; 941: 9³ = 729 → 98

  3. ∛12167 = ?
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    Ends 7 → 3; 12: 2³ = 8 → 23