2. Simplify $\sqrt[3]{10+7 \sqrt{2}}+\sqrt[3]{10-7 \sqrt{2}}$ to get the result $\qquad$ .
2. $2 \sqrt[3]{4}$

Let the original expression $=x>0$. Then
$$
\begin{array}{l}
x^{3}=20+3 \sqrt[3]{100-49 \times 2} \cdot x \\
\Rightarrow x^{3}-3 \sqrt[3]{2} \cdot x-20=0 . \\
\text { Let } x=\sqrt[3]{4} y>0 \text {. Then } \\
4 y^{3}-6 y-20=0 \\
\Rightarrow(y-2)\left(2 y^{2}+4 y+5\right)=0 .
\end{array}
$$

Solving gives $y=2$.
Therefore, the original expression $=2 \sqrt[3]{4}$.