- Cubes from 1- 10
Cube ends with
|Thus as seen cubes have distinct ending, there is no overlapping. Thus, if the given number is perfect cube, then the last digit will help to find the cube root.|
|8 (Compliment of 2)|
|7 (Compliment of 3)|
|3 (Compliment of 7)|
|2 (Compliment of 8)|
- Cube roots need be grouped in a group of 3 from R –> L.Thus the number of groups formed will be == Number of digits in the cube root.For example (for perfect cubes).
- 1728 will be grouped as 1,728. Thus its cube root will be of 2 digits84604519 will be grouped as 84,604,519. Thus its cube root will be of 3 digits.300763 will be grouped as 300,763. Thus its cube root will be of 2 digits.
- Always the 1st group will decide the 1st digit of cube root.Find the perfect cube which is <= 1st group and its cube root will be 1st digit of given number’s cube root.
For above examples
|Cube||Perfect cube <= 1st group||Cube root of column 2||1st digit of given num’s cube root. (3rd point)||Last digit of given num’s cube root.||Number of digits in given num’s cube root (2nd point)||Required cube root|
- As seen from above table, when we have 2 groups we can directly write the cube root(2 digits) i.e. Calculating cube root of a number having <=6 digits is very simple and doesn’t require more steps. But if we have more than 2 groups we need to use some other logic.
- 3 digit number(cba) can be written as a+10b+100c. Its cube:(a+10b+100c)3= a3 + 1000b3 + 10,00,000c3 + 30a2b + 300a2c + 300ab2 + 30,000ac2 + 3,00,000bc2 + 30,000b2c + 6000abc.= 10,00,000c3 + 1,00,000 x 3bc2 + 10,000 x (3ac2+ 3b2c) + 1000 x (b3+6abc) + 100 x (3a2c + 3ab2) + 10 x 3a2b + a3.
3a2c + 3ab2
Argumentation Method (Vedic Math Cube Root for a 3 digit number):
It is a method of eliminating process of reasoning methodical.
- From unit’s place, subtract a3 and this will eliminate last digit.
- From ten’s place, subtract 3a2b and this will eliminate 2nd last digit.
- From hundreds place, subtract (3a2c + 3ab2) and this will eliminate 3nd last digit.
- From Thousands place, subtract (b3+6abc) and this will eliminate 4th last digit and so on.