Find the smallest number by which 4608 must be divided to obtain a perfect cube. Also find the cube root of the number obtained?
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Dear Student, 

  We have, Prime Factorisation of 4608 =  $\underline{2 \times 2 \times 2} \times \underline{ 2 \times 2 \times 2} \times \underline{2 \times 2 \times 2} \times 3 \times 3$
  From above, we found that 3 is not making the pair of three.

  Hence the smallest number by which 4608 must be divided to obtain a perfect cube is $3 \times 3 = 9$.

 Also, 
           $$\begin{gathered} The number obtained after dividing 4608 by the smallest number is : \\ \underline{2 \times 2 \times 2} \times \underline{ 2 \times 2 \times 2} \times \underline{2 \times 2 \times 2} = 512 \\ So, Cube Root of 512 is : \sqrt[3]{512} = 8 \end{gathered}$$

Hope this information clears your doubts.

Regards