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)


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