Cuberoot

1) cuberoot_check

Let’s define something called a Digital root.

It is the sum obtained after iteratively adding the digits of a number, till a single digit remains.

For example,

  • For 345, digital root of 345 => 3 + 4 + 5 =12. Now, 12 => 1+2 = 3.12=1+2=3. So, digital root of 345 = 3.
  • For 12345678, digital root is 1+2+3+4+5+6+7+8 = 36. Now, 3+6 = 9. So, digital root of 12345678 = 9.

Turns out that for all perfect cubes, the digital root will either be 1,8,9. 0 is not included as 0 is a perfect cube of itself.

Anyways, if for a number xx you get a digital root that is not 1,8,9 you can confidently say that xx is NOT a perfect cube.

If the digital root is 1, 8, 9, 0 the number may or may not be a perfect cube.

Implementation:

import vedicpy as vedic

a= vedic.cuberoot.cuberoot_check(123)
print(a)
print(type(a))

>>> False
>>> <class 'bool'>

This function returns a boolean value.

2) cuberoot_under_1000000

cuberoot example

Implementation:

import vedicpy as vedic

a= vedic.cuberoot.cuberoot_under_1000000(175616)
print(a)

>>> 56

Vedic Mathematics doesn’t provide a way to cube root accurately. So, if it says that the number is a perfect cube there is still some chance that it is not.