The value of 1 7 - 6 - 1 6 - 5 + 1 5 - 2 - 1 8 - 7 + 13 - 8 is:

Answer: Option C

$$\begin{array}{rl}& \frac{1}{\sqrt{7}-\sqrt{6}}-\frac{1}{\sqrt{6}-\sqrt{5}}+\frac{1}{\sqrt{5}-2}-\frac{1}{\sqrt{8}-\sqrt{7}}+\frac{1}{3-\sqrt{8}}\\ & \Rightarrow \text{Rationalising}\\ & \Rightarrow \frac{\left(\sqrt{7}+\sqrt{6}\right)}{\left(\sqrt{7}-\sqrt{6}\right)\left(\sqrt{7}+\sqrt{6}\right)}-\frac{\left(\sqrt{6}+\sqrt{5}\right)}{\left(\sqrt{6}-\sqrt{5}\right)\left(\sqrt{6}+\sqrt{5}\right)}+\frac{\left(\sqrt{5}+\sqrt{4}\right)}{\left(\sqrt{5}-\sqrt{4}\right)\left(\sqrt{5}+\sqrt{4}\right)}-\frac{\left(\sqrt{8}+\sqrt{7}\right)}{\left(\sqrt{8}-\sqrt{7}\right)\left(\sqrt{8}+\sqrt{7}\right)}+\frac{\left(\sqrt{9}+\sqrt{8}\right)}{\left(\sqrt{9}-\sqrt{8}\right)\left(\sqrt{9}+\sqrt{8}\right)}\\ & \Rightarrow \frac{\left(\sqrt{7}+\sqrt{6}\right)}{1}-\frac{\left(\sqrt{6}+\sqrt{5}\right)}{1}+\frac{\left(\sqrt{5}+\sqrt{4}\right)}{1}-\frac{\left(\sqrt{8}+\sqrt{7}\right)}{1}+\frac{\left(\sqrt{9}+\sqrt{8}\right)}{1}\\ & \Rightarrow \sqrt{7}+\sqrt{6}-\sqrt{6}-\sqrt{5}+\sqrt{5}+\sqrt{4}-\sqrt{8}-\sqrt{7}+\sqrt{9}+\sqrt{8}\\ & \Rightarrow \sqrt{4}+\sqrt{9}\\ & \Rightarrow 2+3\\ & \Rightarrow 5\end{array}$$