Question

Racionalize os denominadores das expressões:

a) 11/ (3√5 + 2√3)​

Answer 1

$\frac{11}{3\sqrt{5}~+~2\sqrt{3}}~.~\frac{3\sqrt{5}~-~2\sqrt{3}}{3\sqrt{5}~-~2\sqrt{3}}\\\\\\\frac{11~.~(3\sqrt{5}~-~2\sqrt{3})}{3\sqrt{5}~.~3\sqrt{5}~-~3\sqrt{5}~.~2\sqrt{3}~+~2\sqrt{5}~.~3\sqrt{5}~-~2\sqrt{3}~.~2\sqrt{3}}\\\\\\\frac{11~.~(3\sqrt{5}~-~2\sqrt{3})}{3^2\sqrt{5}^2~-~3.2\sqrt{5.3}~+~3.2\sqrt{5.3}~-~2^2\sqrt{3}^2}\\\\\\\frac{11~.~(3\sqrt{5}~-~2\sqrt{3})}{9~.~5~-~4~.~3}\\\\\\\frac{11~.~(3\sqrt{5}~-~2\sqrt{3})}{45~-~12}\\\\\\\frac{11~.~(3\sqrt{5}~-~2\sqrt{3})}{33}$

$\frac{1~.~(3\sqrt{5}~-~2\sqrt{3})}{3}\\\\\\\boxed{\frac{3\sqrt{5}~-~2\sqrt{3}}{3}}\\\\ou\\\\\boxed{\sqrt{5}-\frac{2\sqrt{3}}{3}}$