How to Find Cube Root of a Large Number in 3 Seconds

Last updated: June 27, 2026. For coaching and doubts, contactShortcut Maths, Jadavpur, Kolkata 700032. Call+91-9804490328.

Unit-Digit Reference Table for Cubes (1 to 10)

Pattern: The unit digits 1, 4, 5, 6, 9, 0 remain the same when cubed. The pairs (2,8) and (3,7) swap.

The Foolproof 3-Step Formula

Slash the last 3 digits of the given number.
Find the closest lower perfect cube for the remaining left part. Its cube root gives the tens digit.
Match the unit digit of the original number using the table above. This gives the units digit.

Solved Examples

Step 1: Slash last 3 digits → 12 | 567. Step 2: Closest lower perfect cube to 12 is 8 (2³). Tens digit = 2. Step 3: Unit digit of 567 is 7. From table, 7 ↔ 3. Units digit = 3. Answer: 23 (because 23³ = 12167).

Step 1: Slash → 175 | 616. Step 2: Closest lower cube to 175 is 125 (5³). Tens digit = 5. Step 3: Unit digit 6 ↔ 6. Units digit = 6. Answer: 56.

Step 1: Slash → 110 | 592. Step 2: Closest lower cube to 110 is 64 (4³). Tens digit = 4. Step 3: Unit digit 2 ↔ 8. Units digit = 8. Answer: 48.

Step 1: Slash → 238 | 328. Step 2: Closest lower cube to 238 is 216 (6³). Tens digit = 6. Step 3: Unit digit 8 ↔ 2. Units digit = 2. Answer: 62.

Quick Practice (Answers Below)

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∛328509 = ?
∛50653 = ?
∛474552 = ?

Answers: 1) 69 2) 37 3) 78

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FAQs

No. This trick only works for perfect cubes. For non-perfect cubes, you must use approximation or standard methods.

Remember the pairs: 2↔8 and 3↔7. Everything else stays the same.

SSC CGL/CHSL, Railway NTPC, Bank Clerk and some State PSC exams include simplification questions based on cube roots.

Last updated: June 27, 2026. For coaching in Kolkata, call +91-9804490328.

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