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Q.

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


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a

1

b

2

c

3

d

4 

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 ⇒ 2 3 × 2 3 × 2 2  
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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