Question

Find the cube root of the following number by successive subtraction of number:
1, 7, 19, 37, 61, 91, 127, 169, 217, 271, 331, 397, ... 1728 .

Answer 1

We have: 

1728
1
 1727
7
 1720
19
 1701
 37
 1664
61
 1603
91
 1512
127
 1385
169
 1216
217
999
271
 728
331
 397
397
 0
∵  Subtraction is performed 12 times.
∴ \[\sqrt[3]{1728} = 12\]