What is the smallest number by which 256 must be multiplied to obtain a perfect cube?

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answer is B.

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Detailed Solution

It is required to find the smallest number by which 256 must be multiplied to obtain a perfect cube.
Utilizing prime factorization and grouping the factors in triple form, express the given number as a product of prime factors.

256 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 ⇒ 23 × 23 × 22

We see that the prime factor 2 does not appear in the group of triples.
So, we need one more 2 to make it a cube.
In order to create a perfect cube, 256 must be multiplied by the least number possible, which equals 2.
Therefore, option 2 is correct.

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