Đáp án+Giải thích các bước giải:
`\frac{\sqrt{5-2\sqrt{6}}+\sqrt{8-2\sqrt{15}}}{\sqrt{7+2\sqrt{10}}}`
`=\frac{\sqrt{3-2.\sqrt{3.2}+2}+\sqrt{5-2.\sqrt{5.3}+3}}{\sqrt{5+2\sqrt{5.2}+2}}`
`=\frac{\sqrt{(\sqrt{3}-\sqrt{2})}^2+\sqrt{(\sqrt{5}-\sqrt{3})^2}}{\sqrt{(\sqrt{5}+\sqrt{2})^2}}`
`=\frac{|\sqrt{3}-\sqrt{2}|+|\sqrt{5}-\sqrt{3}|}{|\sqrt{5}+\sqrt{2}|}`
`=\frac{\sqrt{3}-\sqrt{2}+\sqrt{5}-\sqrt{3}}{\sqrt{5}+\sqrt{2}}`
`=\frac{\sqrt{5}-\sqrt{2}}{\sqrt{5}+\sqrt{2}}`
`=\frac{(\sqrt{5}-\sqrt{2})^2}{5-2}`
`=\frac{5+2-2\sqrt{10}}{3}`
`=\frac{7-2\sqrt{10}}{3}`
