Let $a,$ $b,$ $c$ be positive real numbers.  Find the largest possible value of
\[\frac{\sqrt{a} + \sqrt{b} + \sqrt{c}}{\sqrt{a + b + c}}.\]
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Let $a,$ $b,$ $c$ be positive real numbers.  Find the largest possible value of
\[\frac{\sqrt{a} + \sqrt{b} + \sqrt{c}}{\sqrt{a + b + c}}.\]
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

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