Similarly to square roots, this method is only applicable if the given number is a perfect cube

Some things to know before starting- 
1. Cubes of numbers from 1 to 10.
1^3   =  1
2^3   =  8 
3^3   =  27
4^3   =  64
5^3   =  125
6^3   =  216
7^3   =  343
8^3   =  512
9^3   =  729
10^3 =  1000

2. If a perfect cube ends with a certain number, what will its cube root end with (units place)?

If the cube ends with 0, 1, 4, 5, 6 or 9, its cube root will end with the same number
Otherwise, if cube ends with 2, cube root will end with 8 and vice versa
And lastly, if the cube ends with 3, then the cube root will end with 7 and vice versa.


Examples- 
1. 3√1728
(3√1728 denotes cube root of 1728)

Step 1: Divide the number (1728) into 2 parts. The first part will be the first three digits from the right side (728). The other part will be everything that is left, which is just (1) in this case. Name 728 as Y and 1 as X for simplicity.




Step 2: Find out what the cuberoot ends with. Here, we have to look at Y. 728 ends with 8, so its cuberoot will end with 2. Therefore, the units digit of the cuberoot is 2.

Step 3: Find out between which 2 cubes X comes, and then select the smaller number. Here however, X itself is a cube of 1 so will will take 1 as the tens place. 

Now we have 1 as the tens place and 2 as the units place which gives us 12 as the cuberoot of 1728.