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Q.

Which of the numbers is not a perfect cube?


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a

999

b

1000

c

27

d

125 

answer is A.

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Detailed Solution

The given number in option 1 is 999.
Prime factorization is now used to translate the given integer into a product of prime factors.
⇒999=3×3×3×37  
The number 999 is not a perfect cube since 37 is left behind after grouping (making triples).
The given number in option 2 is 1000.
Prime factorization of 1000 is,
⇒1000=10×10×10  
The given number 1000 makes triplets in prime factorization and hence it is a perfect cube.
The given number in option 3 is 27.
Prime factorization of 27 is,
⇒27=3×3×3  
The given number 27 makes triplets in prime factorization, hence it is a perfect cube.
The given number in option 4 is 125.
Prime factorization of 125 is,
⇒125=5×5×5  
The given number 125 makes triplets in prime factorization, hence it is a perfect cube.
Therefore, option 1 is correct.
 
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