A) 5
B) 4
C) 3
D) 2
Correct Answer: A
Solution :
(a): Here, \[\frac{1}{3-\sqrt{8}}=\frac{\left( 3+\sqrt{8} \right)}{\left( 3-\sqrt{8} \right)\left( 3+\sqrt{8} \right)}\] \[=\frac{3+\sqrt{8}}{9-8}=3+\sqrt{8}\] \[\frac{1}{\sqrt{8}-\sqrt{7}}=\frac{\sqrt{8}+\sqrt{7}}{\left( \sqrt{8}-\sqrt{7} \right)\left( \sqrt{8}+\sqrt{7} \right)}\] =\[\sqrt{8}+\sqrt{7}\] and??.. so on Expression =\[(3+\sqrt{8})-(\sqrt{8}+\sqrt{7})+(\sqrt{7}+\sqrt{6})-(\sqrt{6}+\sqrt{5})+(\sqrt{5}+\sqrt{2})\] \[=(3+\sqrt{8})-(\sqrt{8}+\sqrt{7})-\sqrt{7}+\sqrt{7}+\sqrt{6}-\sqrt{6}-\sqrt{5}+\sqrt{5}+2\] \[=3+2=5\]
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