+1286 What is the smallest positive integer n such that \sqrt[4]{1323*n*84*779*5*3*441} is an integer?
+135 Technically, the answer is 0 since sqrt[4](0) = 0, but if that's not it, then the second smallest integer is:
\(\sqrt[4]{1323*n*84*779*5*3*441}\)
\(1323 = 3^3 7^2\)
\(84 = 2^23^17^1\)
\(779 = 19^141^1\)
\(441 = 3^27^2\)
\(\sqrt[4]{1323*n*84*779*5*3*441} = 2^23^85^17^519^141^1\)
To make all exponents a multiple of four, n must be \(2^25^37^319^341^3 = \mathbf{81073047338500}\)
+135 edit: The answer can't be 0 since it must be a positive integer. The second bolded number is the correct answer
