Problem

Find the length of one side of a cube with volume 4361420.8 $m^3$.

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Solution

Prime factorization of 43614208 yields

$$43614208=2^{15}*11^3,$$

$$∴ 42614208=(2^5×11)^3.$$

Therefore, the length of one side of this cube is

$$\sqrt[3]{4361420.8}=\sqrt[3]{42614208×\frac{1}{10}}=2^5×11×\frac{1}{\sqrt[3]{10}}≒163.38392694317.$$

(Answer) approximately 163.3839 $m$.

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Reference

Yoshikazu Yamakawa, ed. (1997) Okayama ken no Sangaku (Sangaku in Okayama Prefecture), p.50; p.311.