$\begin{array}{l}\text { 3. } \frac{1}{2 \sqrt{1}+\sqrt{2}}+\frac{1}{3 \sqrt{2}+2 \sqrt{3}}+\cdots+ \\ \frac{1}{25 \sqrt{24}+24 \sqrt{25}}=\end{array}$
3. $\frac{4}{5}$ Hint: Apply $\frac{1}{(k+1) \sqrt{k}+k \sqrt{k+1}}=$ $\frac{1}{\sqrt{k}}-\frac{1}{\sqrt{k+1}}$, let $k=1,2, \cdots, 24$ be substituted respectively, and the result is obtained.