As you know finding the cube root of non perfect is very difficult, claiming to find cube root of imperfect cubes in 10 seconds is almost impossible. However in this article I will give you two approximation methods to find cube root of an imperfect cube.

First method to find cube root of non – perfect cubes

Step 1- Find the integral part 

how to find cube root of non perfect cube

Step 2- Finding the decimal part of cube root

6 – 5 = 1 and NOW divided by 3 =>1/3= 0.33.

step 3- Add this decimal number to to the integral cube root i.e. 0.3 + 5 = 5.3. Thus the cube root of 150 is 5.3.Now the actual cube root will be 5.314 but this is an approximation method and results will be always correct to only first decimal place.

Let us find cube root of a bigger non- perfect cube number,

for example 968,385

Make triplets of numbers, Ignore last 3 numbers, now check first 3 numbers.

968 is somewhere between cube of 9=729 and cube of 10 =1000, So integral part of cube is 9.

Now divide 968/81=11.9, because 11.9 is greater than 9 so subtract it from 9.

11.9-9=2.9.

Now divide the number by 3, 2.9/3=0.9 (no need to go beyond first digit because method is not accurate beyond first digit and we can’t waste time)

now after adding with integral part 9+0.9=9.9.

So cube root of 968,385 will be close to 99. But from this method it seems that

However this method is certainly not very elegant to present and accuracy has limits . Please let me have your views.

Second method to find cube root of non – perfect cubes

Before I tell you the second method you have to look at the following table,

1. First step is same. Find integral cubes root of which your number is.
2. Now subtract the cube of integral part from the number and suppose this number is x.
3. Divide in the number by (Addition index I) before subtracting (n-1)*Dl/100, that will be your first digit after decimal place. as easy as it gets :).

For example

Step 1- Find the integral part 

Step 2- Finding the decimal part of cube root

step 3- now divide by addition index Ia=7.6 to guess value of n

n= 25/7.6~3, so subtract 25-2*0.49=24.02

Step 4-divide 24.02 by addition index

24.02/7.6= 3.16

so decimal part is0.316 which is lot more accurate. Hence cube root will be 5.316

Let us find cube root of a bigger non- perfect cube number,

for example 968,385

Step one will remain same,968 is somewhere between cube of 9=729 and cube of 10 =1000, So integral part of cube will be between 90 and 100.

Step 2- Finding the decimal part of cube root