Hachiman Wake Shrine (1890), Sako, Akaiwa City, Okayama Prefecture (23)


Problem

What is the sixth root of $59604644775390625$ $\ ?$


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Solution

When $59604644775390625$ is factorized into prime factors, $$59604644775390625=5^{24}=(5^4)^6=625^6.$$ Therefore, we find that $$\sqrt[6]{59604644775390625}=625.$$

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$$Ans. \quad 625$$


Reference

Yoshikazu Yamakawa, ed. (1997) Okayama ken no Sangaku (Sangaku in Okayama Prefecture), p.53; p.295.