A) 5
B) 1
C) 3
D) 0
Correct Answer: A
Solution :
\[\frac{1}{\sqrt{9}-\sqrt{8}}=\frac{1}{\sqrt{9}-\sqrt{8}}\times \frac{\sqrt{9}+\sqrt{8}}{\sqrt{9}+\sqrt{8}}=\frac{\sqrt{9}+\sqrt{8}}{9-8}\] Expression \[=(\sqrt{9}+\sqrt{8})-(\sqrt{8}+\sqrt{7})+(\sqrt{7}+\sqrt{6})-(\sqrt{6}\sqrt{5})\] \[+(\sqrt{5}+\sqrt{4})\] \[=\sqrt{9}+\sqrt{8}-\sqrt{8}-\sqrt{7}+\sqrt{7}+\sqrt{6}-\sqrt{6}-\sqrt{5}\] \[+\sqrt{5}+\sqrt{4}\] \[=\sqrt{9}+\sqrt{4}=3+2=5\]
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