8th Class Mathematics Squares and Square Roots Question Bank Square and Square Roots

  • question_answer 24) Find the value of \[\sqrt{2\sqrt{2\sqrt{2\sqrt{2\sqrt{2}?}}}}\]

    A)  \[{{2}^{\frac{1}{31}}}\]                                

    B)  \[{{2}^{\frac{1}{32}}}\]     

    C) \[{{2}^{\frac{31}{32}}}\]         

    D)  \[{{2}^{\frac{30}{31}}}\]

    Correct Answer: C

    Solution :

    (b): \[y=\sqrt{2\sqrt{2\sqrt{2\sqrt{2\sqrt{2}}}}}\] \[{{y}^{2}}=2\sqrt{2\sqrt{2\sqrt{2\sqrt{2}}}}\] \[{{y}^{4}}=8\sqrt{2\sqrt{2\sqrt{2}}}\] \[{{y}^{8}}=128\sqrt{2\sqrt{2}}\] \[{{y}^{16}}={{\left( 128 \right)}^{2}}\times 2\sqrt{2}\] Then \[{{y}^{32}}={{\left( 128 \right)}^{4}}\times 4\times 2\] \[{{y}^{32}}={{2}^{28+2+1}}={{2}^{31}}\]  \[{{2}^{\frac{31}{32}}}\]

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