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9th Class Mathematics Number System and its Operations Question Bank Number System

  • question_answer
    The value of\[\sqrt{4\sqrt[3]{16\sqrt{4\sqrt[3]{16}\sqrt{4\sqrt[3]{16}}}}}......\]is

    A)  2                                

    B)  \[{{2}^{2}}\]

    C)  23                               

    D)  \[{{2}^{5}}\]

    Correct Answer: B

    Solution :

    (b): \[x=\sqrt{4\sqrt[3]{16\sqrt{4\sqrt[3]{16.........}}}}\] On squaring both sides, \[{{x}^{2}}=4\sqrt[3]{16\sqrt{4\sqrt[3]{16.....}}}\] On cubing, \[{{x}^{6}}=64\times 16x\] \[x=4\]


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