Question

31)Escreva na forma de um único radical e simplifique.
A)√√√7

B)5^√√11

C) 3^√√√3

d) 5^√√32

E) √√√1280

F)√2 x √5

g) √32/2 x √2/4

h) 3^√√√2

Answer 1

Resposta:

$A)\\ \sqrt{\sqrt{\sqrt{7} } } =\sqrt[2.2.2]{7} =\sqrt[8]{7} \\ \\ B)\\ \sqrt[5]{\sqrt{11} } =\sqrt[5.2]{11} =\sqrt[10]{11} \\ \\ C)\\ \sqrt[3]{\sqrt{\sqrt{3} } } =\sqrt[3.2.2]{3} =\sqrt[12]{3} \\ \\ D)\\ \sqrt[5]{\sqrt{32} } =\sqrt[5.2]{32} =\sqrt[10]{2^5} ~~simplificando~~\sqrt[10:5]{2^{5:5}} =\sqrt{2}$

$E)\\ \sqrt{\sqrt{\sqrt{1280} } } =\sqrt[2.2.2]{2^8.5} =\sqrt[8]{2^8.5} =2\sqrt[8]{5} \\ \\ F)\\ \sqrt{2} \times\sqrt{5} =\sqrt{2\times5} =\sqrt{10} \\ \\ G)\\ \sqrt{{32\over2}} \times\sqrt{{2\over4}} =\sqrt{{32\times2\over2\times4}} =\sqrt{{64\over8}} =\sqrt{8} =\sqrt{2^2.2} =2\sqrt{2}$