Question 1209005
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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.



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


We know that {{{5^4}}} = 625,  so we try next integer after 5, which is 6.


{{{6^4}}} = 1296.     <<<------->>>  Such number N is 1296.


So,  n = 1296 - 675 = 621.    <U>ANSWER</U>


<U>CHECK</U>.  {{{root(4, 675+621)}}} = {{{root(4,1296)}}} = 6.
</pre>

Solved, with explanations.