Problem
What is the side length of a square with an area of $85000 ft^2$ ?
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Solution
The prime factorization of $85000$ is:
$$85000=2^3×5^4×17=2^2×5^4×(2×17),$$
$$∴ \ \sqrt{85000}=2×5^2×\sqrt{2×17}≒291.547594742265.$$
$$85000=2^3×5^4×17=2^2×5^4×(2×17),$$
$$∴ \ \sqrt{85000}=2×5^2×\sqrt{2×17}≒291.547594742265.$$
$$(Answer) \qquad approximately \quad 291.5476 \ ft.$$
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Note
However, in the original text, the answer is given as “$291.13875$.”
Reference
Yoshikazu Yamakawa, ed. (1997) Okayama ken no Sangaku (Sangaku in Okayama Prefecture), p.27; p.400.