1974 AMC 12 Question 20

Let $$
\begin{aligned} T={}&\frac1{3-\sqrt8} -\frac1{\sqrt8-\sqrt7}\\ &+\frac1{\sqrt7-\sqrt6} -\frac1{\sqrt6-\sqrt5}\\ &+\frac1{\sqrt5-2}; \end{aligned}
$$ then