Question

Find which of the following number is  cube of rational number 0.001331 .

Answer 1

We have:

\[0 . 001331 = \frac{1331}{1000000} = \frac{11 \times 11 \times 11}{2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 5 \times 5 \times 5 \times 5 \times 5 \times 5} = \frac{{11}^3}{\left( 2 \times 2 \times 5 \times 5 \right)^3} = \frac{{11}^3}{{100}^3} = \left( \frac{11}{100} \right)^3\]

Therefore,

\[0 . 001331\]   is a cube of \[\frac{11}{100}\] .