Computing $\sqrt[4]{28+16 \sqrt 3}$ I want to compute following radical
$$\sqrt[4]{28+16 \sqrt 3}$$
For that, I first tried to rewrite this in terms of exponential. 
$$(28+16\cdot 3^{\frac{1}{2}})^{\frac{1}{4}}$$
We know that $ 28 = 2 \cdot 7^{\frac{1}{2}}$
$$(2 \cdot 7^{\frac{1}{2}}+16\cdot 3^{\frac{1}{2}})^{\frac{1}{4}}$$
However, I'm stuck at this step. Could you assist me?
Regards

\begin{align}
\sqrt[4]{28+16 \sqrt 3}=&\ \sqrt[4]{4(7+2 \sqrt {3\cdot4})}
= \sqrt[4]{4(\sqrt4+\sqrt {3})^2}\\
= &\ \sqrt{4+2\sqrt{1\cdot3}}=\sqrt{(1+\sqrt3)^2}=1+\sqrt3
\end{align}
