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What is the smallest positive integer n such that \sqrt[4]{98 \cdot n} is an integer? If possible, please provide an explanation. THANK YOU!!

Guest Aug 25, 2022

Alan · Answer 1 · 2022-08-25T07:59:06

The fourth root of 98 is between 3 and 4, so the only possible integer values would be 1, 2 or 3 for the fourth root.

So n must be one of $\frac{98}{1^4}$ or $\frac{98}{2^4}$ or $\frac{98}{3^4}$

I'll leave you to determine which of them is an integer.