Q. 5 D3.5( 2 Votes )

Find the smallest number by which each of the following number must be multiplied to obtain a perfect cube.

675

Answer :

675

Prime Factorization:



675 = 5 × 5 × 3 × 3 × 3


= 33 × 52


There are only two 5’s.


675 is not a perfect cube.


To make it a perfect cube, we multiply with 5.


675 × 5 = 3375


= 5 × 5 × 5 × 3 × 3 × 3


= 33 × 53


= 153 which is a perfect cube


The smallest number by which the number 675 must be multiplied to obtain a perfect cube is 5.


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