[คนไม่เก่งที่ชอบคณิต]

4)

$\sqrt{14 + \sqrt{40} + 2\sqrt{15}+ 2\sqrt{35}}$
$= \sqrt{14 + 2\sqrt{2}\sqrt{5} + 2\sqrt{2}\sqrt{7}+ 2\sqrt{5}\sqrt{7}}$
$= \sqrt{2 + 5 + 7 + 2\sqrt{2}\sqrt{5} + 2\sqrt{2}\sqrt{7}+ 2\sqrt{5}\sqrt{7}}$
$= \sqrt{\left( \sqrt{2} +\sqrt{5} + \sqrt{7}\right)^{2}}$
$= \sqrt{2} +\sqrt{5} + \sqrt{7}$

5)
$a = \frac{1}{2}\left(\frac{1}{2\cdot 3} + \frac{1}{3\cdot 4} + \ldots + \frac{1}{19\cdot 20}\right)$
= $\frac{1}{2}\left(\frac{1}{2 }-\frac{1}{ 3} + \frac{1}{3 } - \frac{1}{4} + \ldots + \frac{1}{19 }-\frac{1}{20 } \right)$
= $\frac{1}{2}\left(\frac{1}{2 } -\frac{1}{20 } \right)$ = $\frac{9}{40}$
$b = 2 + 4 + 6 + \ldots + 80$ = $\frac{40}{2}(2+80)$

$4ab = 1476$