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

256

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#### Solution

256 = __2 × 2 × 2__ × __2 × 2 × 2__ × 2 × 2

Here, two 2s are left which are not in a triplet. To make 256 a cube, one more 2 is required.

Then, we obtain

256 × 2 = __2 × 2 × 2__ × __2 × 2 × 2__ × __2 × 2 × 2__ = 512 is a perfect cube.

Hence, the smallest natural number by which 256 should be multiplied to make it a perfect cube is 2.

Concept: Concept of Cube Root

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