How to calculate cube root of a number

How to Calculate Cube root of a number between 11 and 100 in your mind.

Cube root of a number can be a very difficult task specially when it lies in the range of 11 and 100. How would you like if you can do it in your head in two seconds in a competitive exam. It will give you an edge over others.

Now, without taking much of your time. Below is the trick.

Things to remember:
A) Cube of numbers from 1 to 10 i.e

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

Notice that cube of every number ends with itself except(2,3,7,8).

B) Cube of 2 ends with 8 and vice versa. Cube of 3 ends with 7 and vice versa.

 Main Method():


Lets discuss this with an example.

To find out the cube root of  421875

Solution: Let cube root of this number be AB.

we will first find the B with the help of last three digits

B will be the same as the last digit of the question(here 421875) with an exception that
if last digit is 2, B will be 8
if last digit is 8, B will be 2
if last digit is 3, B will be 7
if last digit is 7, B will be 3

Also, last three digits are ignored as soon as we find B.


here, last digit is 5. so, B is 5.

Now to find A, we are left with only 421.

now, 421 lies between 7(cube 343) and 8(cube 512). so, the minimum of these two will be the A(i.e. 3)


Hence answer is 75.

Another example when last digit is either 2,3,7 or 8.

To find out the cube root of  50653.

To find B, Take last three digits. 653
B will be 7 as the last digit is 3.

To find A, Take remaining digits. 50
50 lies between 3(cube 9) and 4(cube 64). SO, the minimum of these two will be A(i.e. 3)

Hence, the answer is 37.


Thank you,
Hope it helps.