Can you find the cube root of a 6-digit perfect cube faster than a calculator? With this method, yes. This guide shows you how to find the cube root of a large number in 3 seconds using a simple unit-digit table and a 3-step formula.
Table of Contents
Unit-Digit Reference Table for Cubes (1 to 10)
| Number | Cube | Unit Digit of Cube | Memory Hook |
|---|---|---|---|
| 1 | 1 | 1 | 1 ↔ 1 |
| 2 | 8 | 8 | 2 ↔ 8 |
| 3 | 27 | 7 | 3 ↔ 7 |
| 4 | 64 | 4 | 4 ↔ 4 |
| 5 | 125 | 5 | 5 ↔ 5 |
| 6 | 216 | 6 | 6 ↔ 6 |
| 7 | 343 | 3 | 7 ↔ 3 |
| 8 | 512 | 2 | 8 ↔ 2 |
| 9 | 729 | 9 | 9 ↔ 9 |
| 10 | 1000 | 0 | 0 ↔ 0 |
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
Example 1: Find ∛12167
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).
Example 2: Find ∛175616
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.
Example 3: Find ∛110592
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.
Example 4: Find ∛238328
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)
- ∛328509 = ?
- ∛50653 = ?
- ∛474552 = ?
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Enquire Now Call 9804490328FAQs
Q1. Does this method work for non-perfect cubes?
No. This trick only works for perfect cubes. For non-perfect cubes, you must use approximation or standard methods.
Q2. How do I memorise the unit-digit table?
Remember the pairs: 2↔8 and 3↔7. Everything else stays the same.
Q3. Which exams ask cube root questions?
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.