I'm doing some self-study and I'm stuck on a proof. Prove that if two open balls on $N$-dimensional Euclidean space are disjoint then $d(x,x') \ge r + r'$
$x$ and $x'$ are the centers of the balls, $r$ and $r'$ are the radii, and the distance between $x$ and $x'$ is given by:
$d(x,x') = \sqrt{ (x_1-x'_1)^2 + (x_2-x'_2)^2 + ...(x_N - x'_N)^2 }$
Also, $x$ and $x'$ are distinct points.