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Railways Quantitative Aptitude Number System and its Operations Sample Paper Number System Sample Test Paper-1

  • question_answer
    Taking \[\sqrt{2}=1.414,\] \[\sqrt{3}=1.732,\] \[\sqrt{5}=2.236,\] and \[\sqrt{6}=2.449,\] find the value of \[\frac{9+\sqrt{2}}{\sqrt{5}+\sqrt{3}}+\frac{6-\sqrt{2}}{\sqrt{5}-\sqrt{3}}\] to the three places of decimal.

    A)  9.2321  

    B)  13.716   

    C)  11.723

    D)  15.892

    Correct Answer: C

    Solution :

    [c] \[\frac{9+\sqrt{2}}{\sqrt{5}+\sqrt{3}}+\frac{6-\sqrt{2}}{\sqrt{5}-\sqrt{3}}\] \[=\frac{9\,(\sqrt{5}-\sqrt{3})+\sqrt{2}\,(\sqrt{5}-\sqrt{3})+6\,(\sqrt{5}+\sqrt{3})-\sqrt{2}\,(\sqrt{5}+\sqrt{3})}{(\sqrt{5}+\sqrt{3})(\sqrt{5}-\sqrt{3})}\]\[=\frac{1}{2}(9\sqrt{5}-9\sqrt{3}+\sqrt{10}-\sqrt{6}+6\sqrt{5}+6\sqrt{3}-\sqrt{10}-\sqrt{6}\]\[=\frac{1}{2}(15\sqrt{5}-3\sqrt{3}-2\sqrt{6})\] \[=\frac{1}{2}[15\times 2.236-3\times 1.732-2\times 2.449]\] \[=\frac{1}{2}[33.540-5.196-4.898]=11.723\]


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