I don’t understand how to approach this problem.

$$h_1, h_2, h_3$$ are three admissible heuristics for an optimisation problem to be solved using A* search. Is the heuristic defined by

$$h(n) = \frac{\sqrt{h_1(n)h_2(n)}+ 2h_3(n)}{3}$$

for any node n of the search graph, admissible?

This is all the information I have, I have no problem specifics or anything else. Any help would be great! Thanks

Let $$f(n)$$ be the optimal cost to node $$n$$. Suppose $$h_1(n) \ldots h_3(n)$$ are positive lower bounds for $$f(n)$$, i.e. admissible heuristics. Can you prove that $$\frac{\sqrt{h_1(n) h_2(n)} + 2 h_3(n)}{3}$$ is no more than $$f(n)$$? You might start by proving that $$\sqrt{h_1(n) h_2(n)} \le f(n)$$.