Algebra

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