Show that (a + b)/2 is greater than or equal to squareroot (ab) for 0 < a ≤ b.

I'm in a class in which I'm being exposed to proofs for the first time, and I'm quite unsure about where to begin.

I can input examples to show that it's true, but that's obviously not what I need to do here.

While I would appreciate a complete explanation, even a gentle nudge in the right direction would be helpful.

Thanks!