What is the smallest positive integer n such that \sqrt[4]{1323*n*84*779*5*3*441} is an integer?

learnmgcat Oct 17, 2024

#1**0 **

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 \(2^25^37^319^341^3 = \mathbf{81073047338500}\)

Maxematics Oct 17, 2024

#2**0 **

edit: The answer can't be 0 since it must be a positive integer. The second bolded number is the correct answer

Maxematics
Oct 17, 2024