Square Root & Cube Root: Tricks
Cube Root – Last Digit Method
Last digit of perfect cubes
- 0³ = 0 → last digit 0,
- 1³ = 1 → last digit 1,
- 2³ = 8 → last digit 8,
- 3³ = 27 → last digit 7
- 4³ = 64 → last digit 4,
- 5³ = 125 → last digit 5,
- 6³ = 216 → last digit 6,
- 7³ = 343 → last digit 3
- 8³ = 512 → last digit 2,
- 9³ = 729 → last digit 9
Rule: Except 2, 3, 7, 8, all digits keep the same last digit in their cube.
Find Cube Root
• Check the last digit → decide unit digit
• Remove last 3 digits → find the range
• Combine both → final answer
1. Exam Trick
Ignore last 3 digits → check cubes → find range → match unit digit
2. Short Note (For Revision)
Cube Root by Last Digit Method
• Last digit decides unit digit of cube root
• Remove last 3 digits to find range
• Compare with nearby perfect cubes
• Combine range + unit digit to get answer
Example:
Q1. Find the cube root of 15625
Options: 20 25 30 35
Ans: 25
Soln
• Last digit = 5 → unit digit = 5
• Ignore last 3 digits → 15
• 2³ = 8, 3³ = 27 → cube root between 20 - 30
Ans = 25
Q2. Find the cube root of 39304
Options: 32 34 36 38
Ans: 34
Soln
• Last digit = 4 → unit digit = 4
• Ignore last 3 digits → 39
• 3³ = 27, 4³ = 64 → cube root between 30 - 40
Ans = 34
Q3. Find the cube root of 35236328
Options: 32 33 34 35
Ans: 32
Soln
• Last digit = 8 → unit digit = 2
• Ignore last 3 digits → 35236
• 32³ = 32768, 33³ = 35937 → lies between these
Ans = 32
Q4. The cube of which number ends in 3 ?
Options: 3 7 9 1
Ans: 7
Soln
7³ = 343 → last digit = 3
Ans = 7
Q5. If the last digit of a cube is 8, the unit digit of its cube root is:
(a) 2 (b) 4 (c) 6 (d) 8
Soln
• 2³ = 8
• 8³ = 512 (last digit 2, not 8)
Ans: (a) 2
Important Rules
• Last digit decides unit digit
• Remaining number decides tens digit
• Except 2, 3, 7, 8, all digits keep the same last digit in cube
• Fast method – no calculation
Q1. What is the cube root of 439039 ?
(a) 67 (b) 69 (c) 89 (d) 79
Ans: (d) 79
Soln
• Last digit = 9 → unit digit of cube root = 9
• Ignore last 3 digits → 439
• 7³ = 343, 8³ = 512
• Cube root lies between 70 - 80 → 79
Q2. What is the cube root of 314432 ?
(a) 62 (b) 66 (c) 68 (d) 64
Ans: (c) 68
Soln
• Last digit = 8 → unit digit = 8
• Ignore last 3 digits → 314
• 6³ = 216, 7³ = 343
• Cube root lies between: 60 - 70 → 68
Q3. What is the cube root of 912673 ?
(a) 93 (b) 97 (c) 87 (d) 107
Ans: (b) 97
Soln
• Last digit = 7 → unit digit = 7
• Ignore last 3 digits → 912
• 9³ = 729, 10³ = 1000
• Cube root lies between 90–100 → 97
Q4. What is the cube root of 373248 ?
(a) 68 (b) 72 (c) 84 (d) 78
Ans: (b) 72
Soln
• Last digit = 8 → unit digit = 2
• Ignore last 3 digits → 373
• 7³ = 343, 8³ = 512
• Cube root lies between 70–80 → 72
Q5. What is the cube root of 175616 ?
(a) 54 (b) 56 (c) 58 (d) 64
Ans: (b) 56
Soln
• Last digit = 6 → unit digit = 6
• Ignore last 3 digits → 175
• 5³ = 125, 6³ = 216
• Cube root lies between 50–60 → 56
Exam Trick
• Last digit → unit digit
• Remaining number → tens digit
• No long calculation needed