Question

find the cube roots of the following numbers by successive subtraction of numbers 1, 7, 19, 37,61,91,127,169,217,271,331,397___
(I)27 (ii) 125 (iii) 512 (iv) 1728​

Answer 1

1. Find the cube roots of the following numbers by successive subtraction of numbers:

1, 7, 19, 37, 61, 91, 127, 169, 217, 271, 331, 397, …

(i) 64

(ii) 512

(iii) 1728

Solution:

(i) 64

Let’s perform subtraction

64 – 1 = 63

63 – 7 = 56

56 – 19 =37

37 – 37 = 0

Subtraction is performed 4 times.

∴ Cube root of 64 is 4.

(ii) 512

Let’s perform subtraction

512 – 1 = 511

511 – 7 = 504

504 – 19 = 485

485 – 37 = 448

448 – 61 = 387

387 – 91 = 296

296 – 127 = 169

169 – 169 = 0

Subtraction is performed 8 times.

∴ Cube root of 512 is 8.

(iii) 1728

Let’s perform subtraction

1728 – 1 = 1727

1727 – 7 = 1720

1720 – 19 = 1701

1701 – 37 = 1664

1664 – 91 = 1512

1512 – 127 = 1385

1385 – 169 = 1216

1216 – 217 = 999

999 – 271 = 728

728 – 331 = 397

397 – 397 = 0

Subtraction is performed 12 times.

∴ Cube root of 1728 is 12.