Example 7 Find the cube root of 3.652264.
From (31) we have
$$\sqrt[3]{3.652264}=\frac{\sqrt[3]{3652264}}{10^{2}}$$

Since $3652264=2^{3} \times 7^{3} \times 11^{3}$, by (32) we get
$$\sqrt[3]{3.652264}=\frac{2 \times 7 \times 11}{100}=1.54$$