Generalizing stuff

Algebra Level 3

Given that $a_1,a_2,\ldots,a_n,b_1,b_2,\ldots,b_n$ are non-negative real numbers that sum to 10, find the minimum possible value of $\left( \sum_{i=1}^{n} \sqrt{a_i^2+b_i^2}\right)^2.$