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प्रश्न
Find the cube root of the following rational number \[\frac{- 125}{729}\] .
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उत्तर
Let us consider the following rational number \[\frac{- 125}{729}\]
Now
\[\sqrt[3]{\frac{- 125}{729}}\]
\[= \frac{\sqrt[3]{- 125}}{\sqrt[3]{729}}\] (∵ \[\sqrt[3]{\frac{a}{b}} = \frac{\sqrt[3]{a}}{\sqrt[3]{b}}\] )
\[= \frac{- \sqrt[3]{125}}{\sqrt[3]{729}}\] ( ∵ \[\sqrt[3]{- a} = - \sqrt[3]{a}\] )
\[= - \frac{5}{9}\] ( ∵ \[729 = 9 \times 9 \times 9 \text{ and } 125 = 5 \times 5 \times 5\]).
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