What is the value of $\sqrt{473+\sqrt{529}+\sqrt{256}+\sqrt{289}}$?

Let's simplify the expression step-by-step from the inside out:
$$\sqrt{529}=23$$
$$\sqrt{256}=16$$
$$\sqrt{289}=17$$
Now substitute these values back into the expression:
$$\sqrt{473+23+16+17}$$
$$\sqrt{473+56}=\sqrt{529}$$
$$\sqrt{529}=23$$