Let $x$ and $y$ be positive real numbers.  Find the minimum value of
\[\frac{\sqrt{(x^2 + y^2)(3x^2 + y^2)}}{xy}.\]
Question:
Let $x$ and $y$ be positive real numbers.  Find the minimum value of
\[\frac{\sqrt{(x^2 + y^2)(3x^2 + y^2)}}{xy}.\]
Answer:
Let's think step by step.

user
1 + \sqrt{3}
Let $x$ and $y$ be positive real numbers.  Find the minimum value of
\[\frac{\sqrt{(x^2 + y^2)(3x^2 + y^2)}}{xy}.\]
train