To find \( \sqrt[3]{0.729} \), we can express 0.729 as a fraction or in a simpler form.
We know that: \[ 0.729 = \frac{729}{1000} \]
Next, we can find the cube root of both the numerator and the denominator: \[ \sqrt[3]{0.729} = \sqrt[3]{\frac{729}{1000}} = \frac{\sqrt[3]{729}}{\sqrt[3]{1000}} \]
Calculating both cubic roots, we have: \[ \sqrt[3]{729} = 9 \quad \text{(since \( 9^3 = 729 \))} \] \[ \sqrt[3]{1000} = 10 \quad \text{(since \( 10^3 = 1000 \))} \]
Therefore: \[ \sqrt[3]{0.729} = \frac{9}{10} = 0.9 \]
Thus, the final result is: \[ \sqrt[3]{0.729} = 0.9 \]