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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