We are asked to expand the expression $(7 + \sqrt{3x})^2$.

1. Problem Description

We are asked to expand the expression $(7 + \sqrt{3x})^2$.

2. Solution Steps

We can use the formula $(a+b)^2 = a^2 + 2ab + b^2$.

In our case, $a = 7$ and $b = \sqrt{3x}$.

$(a+b)^2 = a^2 + 2ab + b^2$

$(7 + \sqrt{3x})^2 = 7^2 + 2(7)(\sqrt{3x}) + (\sqrt{3x})^2$

$= 49 + 14\sqrt{3x} + 3x$

Therefore, the expanded expression is $49 + 14\sqrt{3x} + 3x$.

3. Final Answer

$3x + 14\sqrt{3x} + 49$