Question

Find which of the following number is  cube of rational number \[\frac{125}{128}\] .

 

Answer 1

We have:  \[\frac{125}{128} = \frac{5 \times 5 \times 5}{2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2} = \frac{5^3}{2^3 \times 2^3 \times 2}\]

\[\frac{125}{128}\]  is not a cube of a rational number.