Разность квадратов

$$\sqrt{65^2 - 56^2} = \sqrt{(65-56)(65+56)} = \sqrt{9 \cdot 121} = \sqrt{3^2\cdot11^2} = 3\cdot11 = 33$$

$$a(36a^2 - 25)\left(\dfrac{1}{6a+5} - \dfrac{1}{6a-5}\right) = a(36a^2 - 25) \cdot \dfrac{(6a-5) - (6a+5)}{(6a+5)(6a-5)} =$$ $$= a(36a^2 - 25) \cdot \dfrac{-10}{36a^2 - 25} = a \cdot (-10) = -10a$$ При $a = 36,7$: $$-10 \cdot 36,7 = -367$$

$$(9b^2 - 49)\left(\dfrac{1}{3b-7} - \dfrac{1}{3b+7}\right) + b - 13 = (9b^2 - 49) \cdot \dfrac{(3b+7) - (3b-7)}{(3b-7)(3b+7)} + b - 13 =$$ $$(9b^2 - 49) \cdot \dfrac{14}{9b^2 - 49} + b - 13 = 14 + b - 13 = b + 1$$ При $b = 345$: $$345 + 1 = 346$$

$$\frac{(432-568)(432+568)}{1000} = \frac{(-136)(1000)}{1000} = -136$$

Выполним преобразования:

$$(\sqrt{13}-\sqrt{8})(\sqrt{13}+\sqrt{8})=13-8=5.$$