Let $x,$ $y,$ $z$ be positive real numbers such that $x + y + z = 9.$  Find the maximum value of
\[\sqrt{16 - x^2} + \sqrt{25 - y^2} + \sqrt{36 - z^2}.\]
Question:
Let $x,$ $y,$ $z$ be positive real numbers such that $x + y + z = 9.$  Find the maximum value of
\[\sqrt{16 - x^2} + \sqrt{25 - y^2} + \sqrt{36 - z^2}.\]
Answer:
Let's think step by step.

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12
Let $x,$ $y,$ $z$ be positive real numbers such that $x + y + z = 9.$  Find the maximum value of
\[\sqrt{16 - x^2} + \sqrt{25 - y^2} + \sqrt{36 - z^2}.\]
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