Question

simplifique a expressão 1024.(16+256) ao máximo possível
$\sqrt{1024.( \sqrt{16 + \sqrt{256)} } }$
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Answer 1

$\sqrt{1024\sqrt{16 + \sqrt{256}}} =\\\\\sqrt{1024\sqrt{16 + 16}} =\\\\\sqrt{1024\sqrt{32}} =\\\\\sqrt{1024.\sqrt{2^2.2^2.2}} =\\\\\sqrt{1024.4\sqrt{2}} =\\\\2\sqrt{1024\sqrt{2}} =\\\\2\sqrt{2^{10}\sqrt{2}} =\\\\2.2^5\sqrt\sqrt{2}} =\\\\64\sqrt\sqrt{2}} =\\\\64\sqrt[4]{2} =\\\\2^6.2^{1/4} =\\\\2^{6/4} =\\\\2^{3/2} =\\\\\sqrt{2^3} =\\\\\sqrt{8} =\\\\2\sqrt{2}$