SOLUTION: One of the 22nd roots of 73 786 976 294 838 206 464 is a positive integer. What is this integer, and how was the answer found?

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Question 1131960: One of the 22nd roots of 73 786 976 294 838 206 464 is a positive integer. What is this integer, and how was the answer found?
Answer by ikleyn(52932) About Me  (Show Source):
You can put this solution on YOUR website!
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The given number has 2 + 3*6 = 20 digits - hence, the unknown integer is less than 10.


In addition, it is an even number.


So, there are only these possibilities for the unknown number:  2, 4, 6 and 8.


2 and 4 are too small - I checked it using my MS Excel.


6 gives the last digit 6 in all degrees, so 6 does not work, too.


The last possibility is 8, which is the ANSWER.