Đáp án:
$\dfrac{\sqrt{5}}{\sqrt{2}}$
Giải thích các bước giải:
$\dfrac{5+\sqrt{5}}{\sqrt{10}+\sqrt{\:2}}$
$=\dfrac{\left(5+\sqrt{5}\right)\left(\sqrt{10}-\sqrt{2}\right)}{\left(\sqrt{10}+\sqrt{2}\right)\left(\sqrt{10}-\sqrt{2}\right)}$
$=\dfrac{4\sqrt{10}}{8}$ $=\dfrac{\sqrt{10}}{2}$
$=\dfrac{\sqrt{2}.\:\sqrt{5}}{2}$
$=\dfrac{\sqrt{2}\cdot \sqrt{5}}{\sqrt{2}\cdot \sqrt{2}}$
$=\dfrac{\sqrt{5}}{\sqrt{2}}$
