\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
Let \(a \in \mathbb{K}\) and let \(V_1, V_2, V_3\) be three neighborhoods of \(a\) with respective radii \(r_1 = 1/2\), \(r_2 = 1/3\), \(r_3 = 1/5\) (i.e. \(B(a, r_i) \subset V_i\)). Find an explicit \(r > 0\) such that \(B(a, r) \subset V_1 \cap V_2 \cap V_3\).
Capture an image of your work. AI teacher feedback takes approximately 10 seconds.