Q. 5 C5.0( 1 Vote )

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

72

Answer :

72

Prime Factorization:



72 = 2 × 2 × 2 × 3 × 3


= 23 × 32


There are only two 3’s.


72 is not a perfect cube.


To make it a perfect cube, we have to multiply with 3.


72 × 3 = 2 × 2 × 2 × 3 × 3 × 3


216 = 23 × 33


= 63 which is a perfect cube.


The smallest number by which 72 must be multiplied to obtain a perfect cube is 3.


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