Question

Cube root of 1728 by succesive a subtraction method

Answer 1

Answer:

3 v1728=(3^3x2^3v2^3) I/3 = 3x2x2=12

Answer 2

Answer:

12

Step-by-step explanation:

$\text{Successive Subtraction refers to the term using which we subtract a number continuously.}\\\\\text{Formula for Successive Subtraction is:}\\\\\implies 1 \times \dfrac{n(n-1)}{2} \times 6$

Substituting n = 1, we get:

⇒ 1 + 1 ( 1 - 1 ) / 2 × 6

⇒ 1 + 0 × 6 = 1

At n = 2,

⇒ 1 + [ ( 2 ( 2 - 1 ) / 2 ] × 6

⇒ 1 + [ 2 / 2 ] × 6 = 1 + 6 = 7

At n = 3,

⇒ 1 + [ 3 ( 3 - 1 ) / 2 ] × 6

⇒ 1 + [ 3 ( 2 ) / 2 ] × 6

⇒ 1 + 18 = 19

Similarly the series continues as: 1, 7, 19, 37, 61, 91, 127, 169, 217, 271, 331, 397, etc..

Starting Subtraction we get,

⇒ 1728 - 1 = 1727

⇒ 1727 - 7 = 1720

⇒ 1720 - 19 = 1701

⇒ 1701 - 37 = 1664

⇒ 1664 - 61 = 1603

⇒ 1603 - 91 = 1512

⇒ 1512 - 127 = 1385

⇒ 1385 - 169 = 1216

⇒ 1216 - 217 = 999

⇒ 999 - 271 = 728

⇒ 728 - 331 = 397

⇒ 397 - 397 = 0

Therefore after 12 steps we get 0.

Hence the cube root of 1728 is 12.