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) 64 

(ii) 512 

(iii) 1728

Answer 1

(i) 64 

We have, 

64 – 1 = 63 

63 – 7 = 56 

56 – 19 =37 

37 – 37 = 0 

∵ Subtraction is performed 4 times. 

Hence, cube root of 64 is 4. 

(ii) 512 

We have, 

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. 

Hence, cube root of 512 is 8. 

(iii) 1728 

We have, 

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. 

Hence, cube root of 1728 is 12.