Let $a,$ $b,$ $c$ be positive real numbers.  Find the largest possible value of
\[\frac{\sqrt{a} + \sqrt{b} + \sqrt{c}}{\sqrt{a + b + c}}.\]
Question:
Let $a,$ $b,$ $c$ be positive real numbers.  Find the largest possible value of
\[\frac{\sqrt{a} + \sqrt{b} + \sqrt{c}}{\sqrt{a + b + c}}.\]
Answer:
Let's think step by step.

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\sqrt{3}
Let $a,$ $b,$ $c$ be positive real numbers.  Find the largest possible value of
\[\frac{\sqrt{a} + \sqrt{b} + \sqrt{c}}{\sqrt{a + b + c}}.\]
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