2. Calculate $$\frac{35\sqrt{a} \cdot 6\sqrt{b}}{15ab}$$ при $$a=13, b=6$$.

Let's solve this step-by-step:

1. First, simplify the expression: $$\frac{35\sqrt{a} \cdot 6\sqrt{b}}{15ab}$$.
2. Multiply the coefficients in the numerator: $$35 \times 6 = 210$$.
3. Combine the square roots in the numerator: $$\sqrt{a} \times \sqrt{b} = \sqrt{ab}$$.
4. The expression becomes: $$\frac{210\sqrt{ab}}{15ab}$$.
5. Simplify the fraction by dividing the coefficients: $$210 \div 15 = 14$$.
6. So the expression is $$\frac{14\sqrt{ab}}{ab}$$.
7. We can rewrite $$ab$$ as $$(\sqrt{ab})^2$$.
8. The expression is now $$\frac{14\sqrt{ab}}{(\sqrt{ab})^2}$$.
9. Cancel out one $$\sqrt{ab}$$ from the numerator and denominator: $$\frac{14}{\sqrt{ab}}$$.
10. Now, substitute the given values: $$a=13$$ and $$b=6$$.
11. Calculate $$ab$$: $$13 \times 6 = 78$$.
12. The expression becomes $$\frac{14}{\sqrt{78}}$$.
13. To rationalize the denominator, multiply the numerator and denominator by $$\sqrt{78}$$: $$\frac{14\sqrt{78}}{78}$$.
14. Simplify the fraction by dividing both numbers by their greatest common divisor, which is 2: $$\frac{14 \div 2 \sqrt{78}}{78 \div 2} = \frac{7\sqrt{78}}{39}$$.

Ответ: $$\frac{7\sqrt{78}}{39}$$