Equal to what?

Express the contents of the square root in the form of $a^2+2ab+b^2$ so that it can be factorised to $\left(a+b\right)^2$ .

$\begin{aligned} \sqrt{\frac{7+4\sqrt{3}}{2}} &= \sqrt{\frac{4+4\sqrt{3}+3}{3}} \\ &= \sqrt{\frac{\left(2+\sqrt{3}\right)^2}{2}} \\ &= \frac{2+\sqrt{3}}{\sqrt{2}} \end{aligned}$

Then rationalise the denominator to get $\frac{2\sqrt{2}+\sqrt{6}}{2} _\square$