Let $x,$ $y,$ and $z$ be nonnegative real numbers such that $x + y + z = 5.$  Find the maximum value of
\[\sqrt{2x + 1} + \sqrt{2y + 1} + \sqrt{2z + 1}.\]
Question:
Let $x,$ $y,$ and $z$ be nonnegative real numbers such that $x + y + z = 5.$  Find the maximum value of
\[\sqrt{2x + 1} + \sqrt{2y + 1} + \sqrt{2z + 1}.\]
Answer:
Let's think step by step.

user
\sqrt{39}
Let $x,$ $y,$ and $z$ be nonnegative real numbers such that $x + y + z = 5.$  Find the maximum value of
\[\sqrt{2x + 1} + \sqrt{2y + 1} + \sqrt{2z + 1}.\]
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