SOLUTION: What is the smallest positive integer n such that \sqrt[4]{675 + n} is an integer?

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Question 1209005: What is the smallest positive integer n such that \sqrt[4]{675 + n} is an integer?
Answer by ikleyn(52781) About Me  (Show Source):
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What is the smallest positive integer n such that \sqrt[4]{675 + n} is an integer?
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As I understand the post, the question is about the root of degree 4. 


Find minimal positive integer N, which is perfect 4-th degree, greater than 675.


We know that 5%5E4 = 625,  so we try next integer after 5, which is 6.


6%5E4 = 1296.     <<<------->>>  Such number N is 1296.


So,  n = 1296 - 675 = 621.    ANSWER


CHECK.  root%284%2C+675%2B621%29 = root%284%2C1296%29 = 6.

Solved, with explanations.