Question

The smallest positive integer n for which 864 × n is a perfect cube is 

(a) 1 

(b) 2 

(c) 3 

(d) 4

Answer 1

(b) 2

864 = \(\underline{2 × 2 × 2}\) × 2 × 2 × \(\underline{3 × 3 × 3}\)

Since 2 × 2 is the only in complete triplet, so 864 has to be multiplied by 2 to make it a perfect cube.

\(\Rightarrow\) n = 2