Question

a expressão 2√3/√5-√3 é igual a:

Answer 1

$\dfrac{2\sqrt{3}}{\sqrt{5}-\sqrt{3}}=\dfrac{2\sqrt{3}}{\sqrt{5}-\sqrt{3}}\cdot \dfrac{\sqrt{5}+\sqrt{3}}{\sqrt{5}+\sqrt{3}}=\dfrac{2\sqrt{3}\cdot \sqrt{5}\ +\ 2\sqrt{3}\cdot \sqrt{3}}{\left(\sqrt{5}\right)^{2}-\left(\sqrt{3}\right)^2}=\\ \\ \\ \dfrac{2\sqrt{3\cdot 5}\ +\ 2\sqrt{3\cdot 3}}{5-3}=\dfrac{2\sqrt{15}\ +\ 2\sqrt{9}}{2}=\dfrac{\not 2\sqrt{15}\ +\ \not 2\sqrt{9}}{\not 2}=\\ \\ \\ \sqrt{15}\ +\ \sqrt{9}=\sqrt{15}+3$