Finding The Cube in an easy way

During our Mathematical calculationn, we sometime needs the cube of two digit numbers. Cubes of large numbers are rarely used. In the process explained below we will learn to find the cube of any two digit number just by remembering the cubes of First Ten Natural Numbers only.

To Remember :-
1^3 = 3            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

Steps to find the cube of any two digit numbers:-

I. Write down the cube of Tens digit in a row of 4 figures. The other three numbers in the row of answer should be written in a geometrical ratio in the exact proportion which is there between the digits of the given number.
II. The Second step is to write the two times of 2nd and 3rd number just below the second and third number respectively. Then add up the two rows.

Lets Understand it Using some example below :-

Ex 1. 14^3 = ?
I. Tens digit of the number 14 is 1, so we write 1^3 = 1. Also the ratio between 1 and 4 is 1:4, the next digits will be double the previous one. So, the first row is

1      4      16      64

II. In the above row our 2nd and 3rd digit from right are 16 and 4 respectively. so, we write down 32 and 8 below 16 and 4 respectively.Then add up the two rows. 

                                                               1      4      16      64

                                                                       8      32     

                                                         ------------------------------------

                                                   2       ₁7     ₅4         ₆4     = 2744

Ex. 2: 16^3 = ?

Solution:-     1          6          36          216

                               12         72

                     ----------------------------------------

                     4          ₃0        ₁₂9          ₂₁6         =             4096

Ex. 3:- 34^3 = ?

Solution:-     27          36         48          64

                                  72         96 

                   -----------------------------------------

                     39         ₁₂3        ₁₅0         ₆4        =              39304

Here Ratio between frst digit and 2nd digit is 3:4. Hence, Next numbers should be 4/3 of the previous ones.

Hope You all will like it :)

Try to find cubes of different two digits number using the above method  :)

Note:- Don't use this method to find the cubes of 20,30,40,50,..........