A) 5
B) 7
C) 10
D) 12
Correct Answer: A
Solution :
Rationalising the denominator of each term, expression \[=\frac{1}{3-\sqrt{8}}\times \frac{3+\sqrt{8}}{3+\sqrt{8}}-\frac{1}{\sqrt{8}-\sqrt{7}}\] \[\times \frac{\sqrt{8}+\sqrt{7}}{\sqrt{8}+\sqrt{7}}+\frac{1}{\sqrt{7}-\sqrt{6}}\times \frac{\sqrt{7}+\sqrt{6}}{\sqrt{7}+\sqrt{6}}\] \[-\frac{1}{\sqrt{6}-\sqrt{5}}\times \frac{\sqrt{6}+\sqrt{5}}{\sqrt{6}+\sqrt{5}}+\frac{1}{\sqrt{5}-2}\times \frac{\sqrt{5}+2}{\sqrt{5}+2}\] \[=\frac{3+\sqrt{8}}{{{(3)}^{2}}-{{(\sqrt{8})}^{2}}}-\frac{\sqrt{8}+\sqrt{7}}{{{(\sqrt{8})}^{2}}-{{(\sqrt{7})}^{2}}}\] \[+\frac{\sqrt{7}+\sqrt{6}}{{{(\sqrt{7})}^{2}}-{{(\sqrt{6})}^{2}}}-\frac{\sqrt{6}+\sqrt{5}}{{{(\sqrt{6})}^{2}}-{{(\sqrt{5})}^{2}}}+\frac{\sqrt{5}+2}{{{(\sqrt{5})}^{2}}-{{(2)}^{2}}}\] \[=(3+\sqrt{8})-(\sqrt{8}+\sqrt{7})+(\sqrt{7}+\sqrt{6})\] \[-(\sqrt{6}+\sqrt{5})+(\sqrt{5}+2)\] \[=3+\sqrt{8}-\sqrt{8}+\sqrt{7}+\sqrt{7}+\sqrt{6}\] \[-\sqrt{6}-\sqrt{5}+\sqrt{5}+\sqrt{2}=3+2=5\]
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