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Cube Root of perfect cubes



In vedic maths the technique of cube root is simply so amazing that the students will be able to correctly predict the cube root of a number just by looking at it.

What is cube rooting?

Cubing is multiplying and number by itself and then multiplying answer by the original number once again.

Thus the cube of 2 is 2 X 2 X 2 Answer is 8 represented as 23

The cube of 3 is 3 X 3 X 3 Answer is 27 is represented as 33

In squaring we multiply the number by itself and in cubing we multiply the number twice by itself.

What Cube Rooting is?

From the above example number 8 is the cube of 2 and number 2 is the cbe root of 8.

Similarly number 27 is the cube of 3 and 3 is the cube root of 27.

In this chaper of cube rooting we are to learn to calculate cube root. If you are given number 8, you are to arrive at 2. this is a very simple but we will calculate higher order numbers like 744969, 275616

The technique provided here is to calculate the perfect cubes only. It can not be used to find imperfect cubes.

To use this technique, first you must know the number is a perfect cube.

Method:

Memorize the list table below ;

NUMBER CUBE
1 1
2 8
3 27
4 64
5 125
6 216
7 343
8 512
9 729
10 1000

See the above table,the cube of 1 is 1, 2 is 8 and 3 is 27 and so on

Memorize this list. Now give your attention to the underlined numbers.These numbers have unique relationship amongst themselves..

In the first row, the underlined numbers are 1 and 1. It extablish that if the last digit of the cube is 1 then the last digit of the cube root is also 1.

In the second row the underlined numbers are 2 and 8. It establishes relationship that if the last digit of cube is 8 then the last digit of the cube root is 2. Remember if the last digit of the number is 8 the last digit of its cube-root will always be 2.

Similarly thrd row - if the last digit of cube is 7 then the last digit of the cube-root is 3.

In the last row, when a cube ends in 0, the cube-root also ends in 0.

The Last Digit of the Cube The last Digit of the Cube Root
1 1
2 8
3 7
4 4
5 5
6 6
7 3
8 2
9 9
0 0

From the above table we cab conclude that all cube roots end with the same number as their correspoding cubes except for pairs of 3 & 7 and 8 & 2 which end with each other.

Also keep in mind that whenever you calculate cube root, you must put a slash before last three digits.

If you are find the cube root of 105925 and this 45932 you will write it as 105/925 and 45/932.

Immaterial of the number you will alway put slash before last three digits.

LET US SOLVE CUBE ROOTS

No. 1 2 3 4 5 6 7 8 9 10
Cube 1 8 27 64 125 216 343 512 729 1000

We will be solving the cube root in 2 parts. First we shall solve the right hand part of the answer and then the lft part of the slash. You can solve first the left part also.

Example:

Find the Cube-root of 287496

Step 1: Write 287496 as 287|496

Step 2: We know 496 ends with 6, the cube root also ends with 6. Our answer at this stage is (.......6). This is the right hand part of the answer.

Step 3: Go to left hand part 287. 287 lies in between 216(Cube of 6) and 343 (cube of 7)in our table.

Step 4. Out of the two numbers 6 & 7 take the smaller number and write beside ----6 already ontained from right hand part.

Step 5 The final answer is 66

Example



Find the Cube-Root of 205379

Step 1 Represent 205379 as 205|379

Step 2 The cube ends with 9, cube root also ends with a nine. The answer at this stage is (.............9)

Step 2 Left part is 205. it lies between 125 (Cube of 5) and 216(cube of 6)

Step 3 We are to write the smaller digit. write 5

Answer is 59

Example

Find the Cube-Root of 681472

Step 1 Represent 681472 as 681|472

Step 2 The cube ends with 2, cube root also ends with a 8. The answer at this stage is (.............8)

Step 2 Left part is 681. it lies between 512 (Cube of 8) and 729(cube of 9)

Step 3 We are to write the small digit. write 8

Answer is 88

Example

Find the Cube-Root of 830584



Step 1 Represent 830584 as 830|584

Step 2 The cube ends with 4, cube root also ends with a 4. The answer at this stage is (.............4)

Step 2 Left part is 830. it lies between 729 (Cube of 9) and 1000(cube of 10)

Step 3 We are to write the small digit. write 9

Answer is 94

It is immaterial of the number of the digits inthe cube, the procedure is same.

Example

Find the Cube-Root of 2744

Step 1 Represent 2744 as 2|744

Step 2 The cube ends with 4, cube root also ends with a 4. The answer at this stage is (.............4)

Step 2 Left part is 2. it lies between 1 (Cube of 1) and 8(cube of 2)

Step 3 We are to write the small digit. write 1

Answer is 14

PROCEDURE FOR SOLVING CUBE ROOT OF NUMBERS HAVING MORE THAN 6 DIGITS.

There is no difference in the procedure, we are to just expand the table as below-

No. 9 10 11 12
Cube 729 1000 1331 1728

Example

Find the Cube-Root of 1191016

Step 1 Represent 1191016 as 1191|016

Step 2 The cube ends with 6, cube root also ends with a 6. The answer at this stage is (.............6)

Step 2 Left part is 1191. it lies between 1000 (Cube of 10) and 1331(cube of 11)

Step 3 We are to write the small digit. write 10

Answer is 106

EXERCISE:

Find the cube root of

1. 970299

2. 658503

3. 314432

4. 110592

5. 46656

6. 5832

7. 421875

8. 1030301

9. 132651

10. 238328

11. 250047

12. 941192

13. 474552

14. 24389

15. 32768

16. 9261




Vandana Sachar

About the Author

"Vandana Sachar, M.A. Eco, teaching Vedic Maths for the last 15 years"

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