1. The number of positive integers less than $\sqrt[3]{7+5 \sqrt{2}}-\sqrt[3]{7-5 \sqrt{2}}$ is ( ) .
(A) 1
(B) 2
(C) 3
(D) 4
- 1. B.

Let $x=\sqrt[3]{7+5 \sqrt{2}}-\sqrt[3]{7-5 \sqrt{2}}$. Then
$$
\begin{array}{l}
x^{3}=10 \sqrt{2}-3 x \sqrt[3]{7^{2}-(5 \sqrt{2})^{2}} \\
\Rightarrow x^{3}-3 x-10 \sqrt{2}=0 .
\end{array}
$$

Let $x=\sqrt{2} y$. Then
$$
\begin{array}{l}
2 y^{3}-3 y-10=0 \\
\Rightarrow(y-2)\left(2 y^{2}+4 y+5\right)=0 \\
\Rightarrow y=2 \Rightarrow x=2 \sqrt{2} .
\end{array}
$$

Therefore, there are 2 positive integers less than $x=2 \sqrt{2}$.