Problem 2643. Find out base of following arithmetic operation

Created by Pritesh Shah

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Last Solution submitted on Mar 31, 2023

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J.R.! Menzinger on 27 Oct 2014

is the last one rounded?? should be 12.121??

James on 27 Oct 2014

J.R. I believe that 4 is correct. It translates to 50/8, which is 6.25 in base 10. In base 4, that equals 12.1, as the number behind the decimal is 1/4.

However, I think #3 should be '41^0.3=5', since (presumably) you're trying to take the square root of 41. In base 6, 0.5 is 5/6, and 25^(5/6) is not a rational number in any base.

Please correct me if I'm wrong on this, as it's been a while since I've dealt with base 6 decimals. :-)

Pritesh Shah on 28 Oct 2014

J.R.! Menzinger.. No, it is 12.1 only.
James, I will correct , it is 41^0.5

Pritesh Shah on 28 Oct 2014

James
#3 , assume base is b. and convert to decimal and square on both sides and you will get correct base system.

J.R.! Menzinger on 28 Oct 2014

Ok! I understand... ;-)

The hint: use rationals.

James on 28 Oct 2014

Pritesh, I sent an e-mail with some further questions, as the formatting in the comments section would make it unreadable.

Pritesh Shah on 28 Oct 2014

James, Done... Also, added new test case, which is suggested by you...

James on 28 Oct 2014

Glad I could help. Now I just need to solve the problem! :-)

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Problem 2643. Find out base of following arithmetic operation

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Problem 2643. Find out base of following arithmetic operation

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