Cube Roots of Perfect Cubes

Cubes of 1 to 10

Memorize these — they are the foundation:

n	n³
1	1
2	8
3	27
4	64
5	125
6	216
7	343
8	512
9	729
10	1000

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Last Digit Pattern for Cubes

Cube ends with	Root ends with
1	1
8	2
7	3
4	4
5	5
6	6
3	7
2	8
9	9
0	0

Special pairs to remember:

• 2 ↔ 8 (2³ ends in 8, 8³ ends in 2)
• 3 ↔ 7 (3³ ends in 7, 7³ ends in 3)
• 1, 4, 5, 6, 9, 0 → cube ends with the same digit

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The Split Method (for 2-digit cube roots)

For a number up to 6 digits, the cube root is a 2-digit number. Here's how to find it instantly:

Step 1: Split the number into two groups

Split from the right — take the last 3 digits as one group, remaining digits as another.

Step 2: Units digit

Look at the last digit of the number → use the table above to find the units digit of the root.

Step 3: Tens digit

Look at the left group → find the largest perfect cube ≤ this number. Its cube root is the tens digit.

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Worked Examples

Example 1: ∛5832

• Split: 5 | 832
• Last digit 2 → root ends in 8 (since 8³ ends in 2)
• Left group = 5: largest cube ≤ 5 is 1³ = 1 → tens digit = 1
• ∛5832 = 18 ✓

Example 2: ∛17576

• Split: 17 | 576
• Last digit 6 → root ends in 6
• Left group = 17: largest cube ≤ 17 is 2³ = 8 → tens digit = 2
• ∛17576 = 26 ✓

Example 3: ∛54872

• Split: 54 | 872
• Last digit 2 → root ends in 8
• Left group = 54: largest cube ≤ 54 is 3³ = 27 → tens digit = 3
• ∛54872 = 38 ✓

Example 4: ∛175616

• Split: 175 | 616
• Last digit 6 → root ends in 6
• Left group = 175: largest cube ≤ 175 is 5³ = 125 → tens digit = 5
• ∛175616 = 56 ✓

Example 5: ∛32768

• Split: 32 | 768
• Last digit 8 → root ends in 2
• Left group = 32: largest cube ≤ 32 is 3³ = 27 → tens digit = 3
• ∛32768 = 32 ✓

Example 6: ∛250047

• Split: 250 | 047
• Last digit 7 → root ends in 3
• Left group = 250: largest cube ≤ 250 is 6³ = 216 → tens digit = 6
• ∛250047 = 63 ✓

Example 7: ∛658503

• Split: 658 | 503
• Last digit 3 → root ends in 7
• Left group = 658: largest cube ≤ 658 is 8³ = 512 → tens digit = 8
• ∛658503 = 87 ✓

Example 8: ∛205379

• Split: 205 | 379
• Last digit 9 → root ends in 9
• Left group = 205: largest cube ≤ 205 is 5³ = 125 → tens digit = 5
• ∛205379 = 59 ✓

Example 9: ∛804357

• Split: 804 | 357
• Last digit 7 → root ends in 3
• Left group = 804: largest cube ≤ 804 is 9³ = 729 → tens digit = 9
• ∛804357 = 93 ✓

Example 10: ∛456533

• Split: 456 | 533
• Last digit 3 → root ends in 7
• Left group = 456: largest cube ≤ 456 is 7³ = 343 → tens digit = 7
• ∛456533 = 77 ✓

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Quick Reference: Perfect Cubes for Tens Digit

Tens digit	Cube
1	1
2	8
3	27
4	64
5	125
6	216
7	343
8	512
9	729

Compare the left group against this table to instantly identify the tens digit.

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Practice Problems

#	Find	Answer
1	∛5832	18
2	∛17576	26
3	∛54872	38
4	∛175616	56
5	∛32768	32
6	∛250047	63
7	∛658503	87
8	∛205379	59
9	∛804357	93
10	∛456533	77