Question

Find the cube root of the following rational number \[\frac{- 125}{729}\] .

Answer 1

Let us consider the following rational number \[\frac{- 125}{729}\] 

Now

\[\sqrt[3]{\frac{- 125}{729}}\]

\[= \frac{\sqrt[3]{- 125}}{\sqrt[3]{729}}\] (∵ \[\sqrt[3]{\frac{a}{b}} = \frac{\sqrt[3]{a}}{\sqrt[3]{b}}\] )

 \[= \frac{- \sqrt[3]{125}}{\sqrt[3]{729}}\] ( ∵ \[\sqrt[3]{- a} = - \sqrt[3]{a}\] )

\[= - \frac{5}{9}\] ( ∵ \[729 = 9 \times 9 \times 9 \text{ and }  125 = 5 \times 5 \times 5\]).