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SSC Sample Paper SSC CGL - Sample Paper-21

  • question_answer
    What is \[\frac{1}{\sqrt{9}-\sqrt{8}}-\frac{1}{\sqrt{8}-\sqrt{7}}+\frac{1}{\sqrt{7}-\sqrt{6}}\]\[-\frac{1}{\sqrt{6}-\sqrt{5}}+\frac{1}{\sqrt{5}-\sqrt{4}}\]  equal to?

    A) 0                                 

    B) 1

    C) 5         

    D) \[\frac{1}{3}\]

    Correct Answer: C

    Solution :

    \[\frac{1}{\sqrt{9}-\sqrt{8}}-\frac{1}{\sqrt{8}-\sqrt{7}}+\frac{1}{\sqrt{7}-\sqrt{6}}\] \[-\frac{1}{\sqrt{6}-\sqrt{5}}+\frac{1}{\sqrt{5}-\sqrt{4}}\] (or rationalization) \[=(\sqrt{9}+\sqrt{8})-(\sqrt{8}+\sqrt{7})+\sqrt{7}+\sqrt{6})\] \[-(\sqrt{6}+\sqrt{5})+(\sqrt{5}+\sqrt{4})\] \[=\sqrt{9}+\sqrt{4}=3+2=5\]              


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