Let $a,$ $b,$ and $c$ be real numbers such that $a \ge b \ge c \ge 0$ and $a + b = 16.$  Find the maximum value of
\[\sqrt{c(b - c)} + \sqrt{c(a - c)}.\]
Question:
Let $a,$ $b,$ and $c$ be real numbers such that $a \ge b \ge c \ge 0$ and $a + b = 16.$  Find the maximum value of
\[\sqrt{c(b - c)} + \sqrt{c(a - c)}.\]
Answer:
Let's think step by step.

user
8
Let $a,$ $b,$ and $c$ be real numbers such that $a \ge b \ge c \ge 0$ and $a + b = 16.$  Find the maximum value of
\[\sqrt{c(b - c)} + \sqrt{c(a - c)}.\]
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