2. Given positive numbers $a$ and $b$, the following propositions are given:
(1) If $a=1, b=1$, then $\sqrt{a b} \leqslant 1$;
(2) If $a=\frac{1}{2}, b=\frac{5}{2}$, then $\sqrt{a b} \leqslant \frac{3}{2}$;
(3) If $a=2, b=3$, then $\sqrt{a b} \leqslant \frac{5}{2}$;
(4) If $a=1, b=5$, then $\sqrt{a b} \leqslant 3$.

Based on the information provided by the above propositions, please conjecture: If $a=6, b=7$, then $a b \leqslant$
2. $\left(\frac{13}{2}\right)^{2}$