Question

O valor que devemos adicionar a 12 para obter o quadrado de raiz de 5 + raiz de 7​

Answer 1

$12+x~=~\left(\sqrt{5}+\sqrt{7}\right)^2\\\\\\12+x~=~\left(\sqrt{5}+\sqrt{7}\right).\left(\sqrt{5}+\sqrt{7}\right)\\\\\\12+x~=~\sqrt{5}^2+\sqrt{5}.\sqrt{7}+\sqrt{5}.\sqrt{7}+\sqrt{7}^2\\\\\\12+x~=~5+2.\sqrt{5}.\sqrt{7}+7\\\\\\12+x~=~12+2.\sqrt{5~.~7}\\\\\\x~=~12+2\sqrt{5~.~7}-12\\\\\\x~=~2\sqrt{5~.~7}~~~~\rightarrow~passando~o~"2"~para~dentro~da~raiz\\\\\\x~=~\sqrt{4~.~5~.~7}\\\\\\\boxed{x~=~\sqrt{140}}$