2.023. $\sqrt[4]{6 x(5+2 \sqrt{6})} \cdot \sqrt{3 \sqrt{2 x}-2 \sqrt{3 x}}$.

2.023. $\sqrt[4]{6 x(5+2 \sqrt{6})} \cdot \sqrt{3 \sqrt{2 x}-2 \sqrt{3 x}}$.
## Solution.

Domain of definition: $x \geq 0$.

$$
\begin{aligned}
& \sqrt[4]{6 x(5+2 \sqrt{6})} \cdot \sqrt{3 \sqrt{2 x}-2 \sqrt{3 x}}=\sqrt[4]{6 x(5+2 \sqrt{6})} \cdot \sqrt{\sqrt{6 x}(\sqrt{3}-\sqrt{2})}= \\
& =\sqrt[4]{6 x(5+2 \sqrt{6})} \cdot \sqrt[4]{(\sqrt{6 x}(\sqrt{3}-\sqrt{2}))^{2}}=\sqrt[4]{6 x(5+2 \sqrt{6})} \cdot \sqrt[4]{6 x(5-2 \sqrt{6})}= \\
& =\sqrt[4]{6 x(5+2 \sqrt{6}) \cdot 6 x(5-2 \sqrt{6})}=\sqrt[4]{36 x^{2}(25-24)}=\sqrt[4]{36 x^{2}}=\sqrt{6 x}
\end{aligned}
$$

Answer: $\sqrt{6 x}$.