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Question

# 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 coresponding cube roots?

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Solution

## We have examined in question 2, the numbers 130, 345 and 792 are not perfect cubes. therefore (i)130130−1=129129−7=122122−19=103103−37=6666−61=5 here 5 is left ∵5<9 ∴ 5 is to be subtracted to get a perfect cube ∴ Cube root of 130 - 5 = 125 is 5 (i)345345−1=344344−7=337337−19=318318−37=281281−61=220220−91=129129−127=2 Here 2 is left∵2<169 ∴ Cube root of 345−2=343is7 ∴2 is to be subtracted to get a perfect cube (iii)792792−1=791791−7=784784−19=765765−37=728728−61=667667−91=576576−127=449449−169=280280−217=63∴63<217 ∴63 is to be subtracted ∴ Cube root of 792 - 63 = 729 is 9

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