$$
\begin{array}{l}
\text { 1. Let } \\
A=\frac{8}{3} \sqrt{2 \sqrt{13}-5}+2 \sqrt{2 \sqrt{13}-2}, \\
B=\frac{2}{3} \sqrt{2 \sqrt{13}-5}+2 \sqrt{2 \sqrt{17}+7} .
\end{array}
$$

Then $A-B$ can be simplified to
$$
\begin{array}{l}
\text { II, 1.0. } \\
\begin{aligned}
A-B= & 2 \sqrt{2 \sqrt{13}-5}+2 \sqrt{2 \sqrt{13}-2} \\
& -2 \sqrt{2 \sqrt{13}+7} .
\end{aligned}
\end{array}
$$

Below we prove
$$
\sqrt{2 \sqrt{13}-5}+\sqrt{2 \sqrt{13}-2}=\sqrt{2 \sqrt{13}+7} \text {. }
$$

Squaring, we get $\sqrt{62-14 \sqrt{13}}=7-\sqrt{13}$.
Squaring again, we get 62-14 $\sqrt{13}=62-14 \sqrt{13}$.
Therefore, $A-B=0$.