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

Question 1209005: What is the smallest positive integer n such that \sqrt[4]{675 + n} is an integer?

Answer by ikleyn(52781) (Show Source): You can put this solution on YOUR website!
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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  = 625,  so we try next integer after 5, which is 6.


 = 1296.     <<<------->>>  Such number N is 1296.


So,  n = 1296 - 675 = 621.    ANSWER


CHECK.   =  = 6.

Solved, with explanations.

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