• # question_answer 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)  ${{2}^{\frac{30}{31}}}$

(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 ${{y}^{32}}={{\left( 128 \right)}^{4}}\times 4\times 2$ ${{y}^{32}}={{2}^{28+2+1}}={{2}^{31}}$  ${{2}^{\frac{31}{32}}}$