Problem

Find the length of a side of a square with an area of 542726.89 $m^2$.

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Solution

Prime factorization of 54272689 yields

$$54272689=53^2×139^2.$$

So the side length of this square is

$$\sqrt{542726.89}=\sqrt{54272689×\frac{1}{100}}=53×139×\frac{1}{10}=736.7 m.$$

(Answer) 736.7 $m$.

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Reference

Yoshikazu Yamakawa, ed. (1997) Okayama ken no Sangaku (Sangaku in Okayama Prefecture), p.50; p.312.