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
(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.