| Find out the value of \[\frac{1}{\sqrt{9}-\sqrt{8}}-\frac{1}{\sqrt{8}-\sqrt{7}}+\frac{1}{\sqrt{7}-\sqrt{6}}\] \[-\frac{1}{\sqrt{6}-\sqrt{5}}+\frac{1}{\sqrt{5}-\sqrt{4}}\] |
A) 0
B) 5
C) 7
D) 8
Correct Answer: B
Solution :
| \[\frac{1}{\sqrt{9}-\sqrt{8}}-\frac{1}{\sqrt{8}-\sqrt{7}}+\frac{1}{\sqrt{7}-\sqrt{6}}\] |
| \[-\,\,\frac{1}{\sqrt{6}-\sqrt{5}}+\frac{1}{\sqrt{5}-\sqrt{4}}\] |
| \[\therefore \]\[\frac{1}{\sqrt{9}-\sqrt{8}}\times \frac{(\sqrt{9}+\sqrt{8})}{(\sqrt{9}+\sqrt{8})}=\frac{\sqrt{9}+\sqrt{8}}{9-8}=\sqrt{9}+\sqrt{8}\] |
| Similarly, |
| \[\frac{1}{\sqrt{8}-\sqrt{7}}=\sqrt{8}+\sqrt{7};\,\,\]\[\frac{1}{\sqrt{7}-\sqrt{6}}=\sqrt{7}+\sqrt{6}\] |
| \[\frac{1}{\sqrt{6}-\sqrt{5}}=\sqrt{6}+\sqrt{5}\]and \[\frac{1}{\sqrt{5}-\sqrt{4}}=\sqrt{5}+\sqrt{4}\] |
| \[\therefore \] Above given expression can be written as, |
| \[\sqrt{9}+\sqrt{8}-(\sqrt{8}+\sqrt{7})+(\sqrt{7}+\sqrt{6})\] |
| \[-\,\,(\sqrt{6}+\sqrt{5})+(\sqrt{5}+\sqrt{4})\] |
| \[\Rightarrow \]\[\sqrt{9}+\sqrt{8}-\sqrt{8}-\sqrt{7}+\sqrt{7}+\sqrt{6}-\sqrt{6}-\sqrt{5}+\sqrt{5}+\sqrt{4}\] |
| \[\Rightarrow \] \[\sqrt{9}+\sqrt{4}=3+2=5\] |
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