Question

$\sqrt[2]{(2 + 1)( {2}^{2} + 1)( {2}^{4} + 1)( {2}^{8} + 1) + 1 }$

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Answer 1

$\huge{\purple{❥}\pink{Q}\orange{ʊ}\blue{ᶓ}\red{ʂ}\green{ȶ}\purple{ɪ}\pink{ø}\red{ɲ}}$

$\small \boxed{ \sqrt[2]{(2 + 1)( {2}^{2} + 1)( {2}^{4} + 1)( {2}^{8} + 1) + 1 } }$

$\huge{\purple{❥}\pink{Á}\orange{ɳ}\blue{ʂ}\red{ɰ}\green{ᶓ}\purple{ɾ}}$

$= \sqrt{(3)(4 + 1)(16 + 1)(64 + 1) + 1} \\ \\ = \sqrt{(3)(5)(17)(65) + 1} \\ \\ = \sqrt{15 \times 1105 + 1} \\ \\ = \sqrt{16575 + 1} \\ \\ = \boxed{ \sqrt{16576} }$