(i) 130
Applying subtraction method, We have,
130 – 1 = 129
129 – 7 = 122
122 – 19 = 103
103 – 37 = 66
66 – 61 = 5
∵ Next number to be subtracted is 91, which is greter than 5
Hence,
130 is not a perfect cube.
(ii) 345
Applying subtraction method, We have,
345 – 1 = 344
344 – 7 = 337
337 – 19 = 318
318 – 37 = 281
281 – 61 = 220
220 – 91 = 129
129 – 127 = 2
∵ Next number to be subtracted is 169, which is greter than 2
Hence,
345 is not a perfect cube
(iii) 792
Applying subtraction method, We have,
792 – 1 = 791
791 – 7 = 784
784 – 19 = 765
765 – 37 = 728
728 – 61 = 667
667 – 91 = 576
576 – 127 = 449
449 – 169 = 280
280 – 217 = 63
∵ Next number to be subtracted is 271, which is greter than 63
Hence,
792 is not a perfect cube
(iv) 1331
Applying subtraction method, We have,
1331 – 1 = 1330
1330 – 7 = 1323
1323 – 19 = 1304
1304 – 37 = 1267
1267 – 61 = 1206
1206 – 91 = 1115
1115 – 127 = 988
988 – 169 = 819
819 – 217 = 602
602 – 271 = 331
331 – 331 = 0
∵ Subtraction is performed 11 times.
Hence,
1331 is a perfect cube
