number theory

it is not a perfect cube

I do not under stand the second part of your question....   divideng by .912847483    will make it a perfect cube of 22

    dividinb by  .07776   will make it a perfect cube of 50 

        etc etc   etc 

If by "find the smallest number", you mean "find the smallest integer", then:

 

9720 = 2^3 * 3^5 * 5 and the smallest integer =3^2 x 5 = 45

 

9720 / 45 =2^3 x 3^3 = 216 - which is a perfect cube of 6.

 

Is 9720 a perfect cube ? If not find the smallest number by which it should be divided to get a perfect cube​    

 

 

Are fractions eligible as "numbers"?  Divide 9720 by 0.00972 to get 1,000,000 which is 100³. 

 

There's no reason to stop there.  Just keep adding zeros between the decimal point and the 9. 

 

You never reach a smallest number. 

_.