Find the cube root of the following numbers by successive subtraction of numbers 1.7.9.
(a) 27
(b) 125
(c) 1,000
(d) 1,331
following numbers by finding their ones and tens digits:
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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.
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