MathematicsIs 9261 a perfect cube? In case of a perfect cube, find the number whose cube it is.

Is 9261 a perfect cube? In case of a perfect cube, find the number whose cube it is.


  1. A
    No
  2. B
    Yes, 21
  3. C
    Yes, 12
  4. D
    Yes, 26 

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    Solution:

    A perfect cube can be expressed as a product of three same numbers
    Now by resolving the given number into prime factors we get,
    9261 = 3 × 3 × 3 × 7 × 7 × 7
    9261 a perfect cube.
    Now, solving further, by converting the group of triplets as a single prime factor, we get,
    92613 =3×7=21
    Hence,  9261 is the cube of  21.
    Therefore, the required answer is:
    Yes,
    9261 is a perfect cube and the cube root of 9261 is 21.
     
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