<s>[INST] 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
 [/INST] Hint:
Try to write
$$28+16 \sqrt 3=(a+b\sqrt 3)^4$$
for suitable $a$ and $b$.
You obtain, reordering the terms
\begin{align}
(a+b\sqrt 3)^4&=(a^4+18a^2b^2+9b^4)+4ab(a^2+3b^2)\sqrt 3.\\
\end{align}
Can you choose $a$ and $b$ so that
$$a^4+18a^2b^2+9b^4=28,\quad ab(a^2+3b^2)=4?$$
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