Question

Cube root of 1728 by successful subtraction method

Answer 1

successive subtraction method we subtract numbers that we obtain from ( 1 + n ( n - 1 )

×

3 )

As :   At n = 1  We get  1 + 1( 1 - 1 )

×

3  = 1 + 0 =  1

At n   = 2 we get 1 + 2 ( 2 - 1 )

×

3  = 1 + 2

×

1 

×

3  = 1 + 6 =  7

At n= 3 we get 1 + 3 ( 3 - 1 )

×

3  = 1 + 3

×

2

×

3  = 1 + 18 =  19

So, we get : 1 , 7 , 19 , 37 , 61 , 91 , 127 , 169 , 217 , 271 , 331 , 397 , . . .

So,

1 ) 1728 - 1 = 1727

2 ) 1727 - 7 = 1720

3 ) 1720 - 19 = 1701

4  ) 1701 - 37 = 1664

5 ) 1664 - 61 = 1603

6 ) 1603  - 91 = 1512

7 ) 1512 - 127 = 1385

8 ) 1385 - 169 = 1216

9 ) 1216- 217 = 999

10 ) 999  - 271 = 728

11 ) 728 - 331 = 397

12 ) 397 - 397 = 0

Here we can see that in 12 subtraction we get " 0 " , So

1728= 12                                                                                  ( Ans )