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

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Question 1209035: What is the smallest positive integer n such that \sqrt[4]{675 + n} is an integer?
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


We want root%284%2C675%2Bn%29 to be an integer.

5^4 = 625, which is less than 675.

6^4 = 1296, which is greater than 675.

675+n = 1296
n = 1296-675 = 621

ANSWER: 621