Cube Root Trick

The Factorising method The Trick Method More Mathemagic

Find the cube root of 79,507 in 5 seconds?

Chelsea Football Club's Liam Delap calculating cube roots of large numbers in his head.

Memorise Just Nine Cubes

This remarkable technique works for any number whose cube root falls between 1 and 100. The secret lies in first memorising the cubes of numbers 1 to 9.

1³ = 1

2³ = 8

3³ = 27

4³ = 64

5³ = 125

6³ = 216

7³ = 343

8³ = 512

9³ = 729

Important: You must memorise these cubes completely. Spend a few minutes learning them - it's the only "work" required for this amazing technique!

Practice Flashcards

Master the cubes 1³ to 9³ with these interactive flashcards:

3³

Cards Completed: 0

The Secret Pattern: Last Digit Pairs

Here's the magic: certain digits have special relationships when cubed. Notice the pattern in the last digits:

2 ↔ 8

3 ↔ 7

1 → 1

4 → 4

5 → 5

6 → 6

9 → 9

                Key Insight: When the last digit is 2, the cube root ends in 8. When it's 8, the cube root ends in 2. Same with 3↔7. The others (1,4,5,6,9) map to themselves!
            

The Two-Step Method

1 Find the Last Digit: Look at the final digit of your number and use the pairing rules to determine the last digit of your cube root.

2 Find the First Digit(s): Remove the last three digits from your number. Find the largest cube from your memorized list that doesn't exceed this remaining number.

Let's see this in action with several examples:

Example 1: Find ∛21,952

21,952

1 Last digit is 2 → Cube root ends in 8 (using the 2↔8 pair)

2 Remove last three digits: 21,952
We have 21 remaining

3 Find the largest cube ≤ 21:
2³ = 8 ✓ (fits)
3³ = 27 ✗ (too big)
So we use 2

∛21,952 = 28

Example 2: Find ∛175,464

175,464

1 Last digit is 4 → Cube root ends in 4 (4 maps to itself)

2 Remove last three digits: 175,464
We have 175 remaining

3 Find the largest cube ≤ 175:
5³ = 125 ✓ (fits)
6³ = 216 ✗ (too big)
So we use 5

∛175,464 = 54

Example 3: Find ∛571,787

571,787

1 Last digit is 7 → Cube root ends in 3 (using the 3↔7 pair)

2 Remove last three digits: 571,787
We have 571 remaining

3 Find the largest cube ≤ 571:
8³ = 512 ✓ (fits)
9³ = 729 ✗ (too big)
So we use 8

∛571,787 = 83

Master the Technique

                Pro Tips:

                • Practice with the pairing rules until they're automatic

                • The hardest part is memorizing the 9 cubes - but it only takes a few minutes

                • Start with smaller examples to build confidence

                • This works for ANY number whose cube root is between 1-100

∛39304

☐ ☐ ✓ ✗

∛27000

☐ ☐ ✓ ✗

∛64000

☐ ☐ ✓ ✗

∛195112

☐ ☐ ✓ ✗

∛1000

☐ ☐ ✓ ✗

∛50653

☐ ☐ ✓ ✗

∛157464

☐ ☐ ✓ ✗

∛5832

☐ ☐ ✓ ✗

∛185193

☐ ☐ ✓ ✗

∛125000

☐ ☐ ✓ ✗

∛13824

☐ ☐ ✓ ✗

∛512000

☐ ☐ ✓ ✗

Check

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