Question

Se x = raíz de 8 - raíz de 72 + 5 raíz de 2 e y = raíz de 2, determine x + y

Answer 1

$x~=~\sqrt{8}~-~\sqrt{72}~+~5\sqrt{2}\\\\\\x~=~\sqrt{2~.~2~.~2}~-~\sqrt{2~.~2~.~2~.~3~.~3}~+~5\sqrt{2}\\\\\\x~=~\sqrt{2^2~.~2}~-~\sqrt{2^2~.~3^2~.~2}~+~5\sqrt{2}\\\\\\x~=~2\sqrt{2}~-~2~.~3\sqrt{2}~+~5\sqrt{2}\\\\\\x~=~2\sqrt{2}~-~6\sqrt{2}~+~5\sqrt{2}\\\\\\\boxed{x~=~\sqrt{2}}$

$x+y~=~\sqrt{2}~+~\sqrt{2}~=~\boxed{2\sqrt{2}}$