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

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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