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SSC Sample Paper SSC CGL - Sample Paper-19

  • question_answer
    Which of the following is a perfect square as well as a cube? 343, 125, 81 or 64

    A) 81                                

    B) 125

    C) 343                              

    D) 64

    Correct Answer: D

    Solution :

    In the given numbers, 64 is only number which is a perfect square as well as a perfect cube. Let        \[x=\sqrt{6+\sqrt{6+...}}\] \[\Rightarrow \]   \[{{x}^{2}}=\sqrt{6+x}\] \[\Rightarrow \]   \[{{x}^{2}}-x-6=0\] \[\Rightarrow \]   \[{{x}^{2}}-3x+2x-6=0\] \[\Rightarrow \]   \[(x-3)(x+2)=0\] \[\Rightarrow \]   \[x=3\]              \[(\because \,\,x\ne -\,2)\]


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