Let $a$ and $b$ be the positive roots of $x^2 - 3x + 1 = 0.$  Find
\[\frac{a}{\sqrt{b}} + \frac{b}{\sqrt{a}}.\]
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Let $a$ and $b$ be the positive roots of $x^2 - 3x + 1 = 0.$  Find
\[\frac{a}{\sqrt{b}} + \frac{b}{\sqrt{a}}.\]
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
2 \sqrt{5}
Let $a$ and $b$ be the positive roots of $x^2 - 3x + 1 = 0.$  Find
\[\frac{a}{\sqrt{b}} + \frac{b}{\sqrt{a}}.\]
train