Đáp án: $\dfrac{\sqrt{5}-\sqrt{2}}{\sqrt{2}+\sqrt5}$
Giải thích các bước giải:
Ta có:
$\dfrac{\sqrt{5-2\sqrt{6}}+\sqrt{8-2\sqrt{15}}}{\sqrt{7+2\sqrt{10}}}$
$=\dfrac{\sqrt{3-2\sqrt{3}\cdot\sqrt{2}+2}+\sqrt{5-2\sqrt{5}\cdot \sqrt{3}+3}}{\sqrt{2+2\sqrt{2}\cdot\sqrt5+5}}$
$=\dfrac{\sqrt{(\sqrt{3}-\sqrt{2})^2}+\sqrt{(\sqrt{5}- \sqrt{3})^2}}{\sqrt{(\sqrt{2}+\sqrt5)^2}}$
$=\dfrac{(\sqrt{3}-\sqrt{2})+(\sqrt{5}- \sqrt{3})}{(\sqrt{2}+\sqrt5)}$
$=\dfrac{\sqrt{5}-\sqrt{2}}{\sqrt{2}+\sqrt5}$
