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Vedic Mathematics:To find cube root of a cubic number within seconds

Naimish K.
28/02/2017 0 0

To find cube root of a cubic numbers:

What are cubic numbers

cube of 1= 1, (ends with 1),cube of 11=   1331   (ends with 1), and so on.

cube of 2= 8, (ends with 8),cube of 12=    1728  (ends with 8), and so on.

cube of 3= 27, (ends with 7),cube of 13=   2147   (ends with 7), and so on.

cube of 4= 64,(ends with 8),cube of 148  (ends with 4), and so on...

cube of 5= 125,(ends with 8),cube of 15 (ends with 5), and so on...

cube of 6= 216,(ends with 8),cube of 16 (ends with 6), and so on...

cube of 7= 343,(ends with 8),cube of 17 (ends with 3), and so on...

cube of 8= 512,(ends with 8),cube of 18 (ends with 2), and so on...

cube of 9= 729,(ends with 8),cube of 19 (ends with 9), and so on...

cube of 10= 1000, cube of 20=  8000, cube of 30=  27000, cube of 40 = 64000, and so on.

To find the cube root of  a cubic number (lets take the cubic number at most of 6- digits)

1 Take triplets from right.

2  decide the unit place of the cuberoot by looking at the unit place of the cube number.

Unit's place in the cubic number                  Unit's place in the cubic number

                     1                                                        1

                      2                                                         8

                      3                                                         7

                     4                                                           4

                     5                                                           5

                     6                                                          6

                     7                                                          3

                    8                                                          2

                    9                                                          9

           ends with 3 zeros                                          ends with one zero

   and so on.

3  decide the 10's place of the cuberoot by looking at the the cube number.

the cubic number(x)                  Unit's place in the cubic number

          0≤x

        1000≤x

        8000≤x

         27000≤x

      64000≤x

            125000≤x

        216000≤x

        343000≤x

         512000≤x

      729000≤x

and so on.

Example-

    Find cuberoot of  314432.

     314432 ends with 2,  so unit place of cuberoot of 314432 is 8.

  216000≤314432

So cuberoot of 314432 i= 68.

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