Find the smallest number that must be subtracted from those of the numbers in question 2 which are not perfect cubes, to make them perfect cubes. What are the corresponding cube roots?
In previous question there are three numbers which are not perfect cubes.
i) 130
Apply subtraction method,
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. So, to make it perfect cube we subtract 5 from it.
130 – 5 = 125 (which is a perfect cube of 5)
ii) 345
Apply subtraction method,
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. So, to make it a perfect cube we subtract 2 from it.
345 – 2 = 343 (which is a perfect cube of 7)
iii) 792
Apply subtraction method,
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. So, to make it a perfect cube we subtract 63 from it.
792 – 63 = 729 (which is a perfect cube of 9)