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SSC Sample Paper Mock Test-13 SSC CGL Tear-II Paper-1

  • question_answer
    \[\left( \frac{1+\sqrt{2}}{\sqrt{5}+\sqrt{3}}+\frac{1-\sqrt{2}}{\sqrt{5}-\sqrt{3}} \right)\]simplifies to

    A)  \[\sqrt{5}+\sqrt{6}\]

    B)  \[2\sqrt{5}+\sqrt{6}\]

    C)  \[\sqrt{5}-\sqrt{6}\]

    D)  \[2\sqrt{5}-3\sqrt{6}\]

    Correct Answer: C

    Solution :

    Given expression \[=\frac{1+\sqrt{2}}{\sqrt{5}+\sqrt{3}}+\frac{1-\sqrt{2}}{\sqrt{5}-\sqrt{3}}\] \[=\frac{(1+\sqrt{2})(\sqrt{5}-\sqrt{3})+(\sqrt{5}+\sqrt{3})(1-\sqrt{2})}{(\sqrt{5}+\sqrt{3})(\sqrt{5}-\sqrt{3})}\]             \[=\frac{\sqrt{5}+\sqrt{10}-\sqrt{3}-\sqrt{6}+\sqrt{5}+\sqrt{3}-\sqrt{10}-\sqrt{6}}{5-3}\]             \[=\frac{2\sqrt{5}-2\sqrt{6}}{2}=\frac{2(\sqrt{5}-\sqrt{6})}{2}=\sqrt{5}-\sqrt{6}\]


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