Q:what will be the smallest number by

which 256 must be multiplied to

obtain a perfect cube

We know the factors of 256 are 2$\times$2$\times$2$\times$2$\times$2$\times$2$\times$2$\times$2, combining them in groups of 3, we see that we are left with 2$\times$2. Thus to make 256 a perfect cube, should multiply it by 2. Thus,

256$\times$2 = 2$\times$2$\times$2$\times$2$\times$2$\times$2$\times$2$\times$2$\times$2.

We can see 256$\times$2 = 512 is a cube of 8.