Đáp án:
$A = \dfrac{\sqrt{10} - \sqrt{6}}{2}$
Giải thích các bước giải:
$A = \sqrt{4 - \sqrt{15}} \to A = \dfrac{\sqrt{2}\sqrt{4 - \sqrt{15})}}{\sqrt{2}}$
$\dfrac{A}{\sqrt{2}} = \dfrac{\sqrt{2(4 - \sqrt{15})}}{\sqrt{2}}$
$= \dfrac{\sqrt{8 - 2\sqrt{15}}}{\sqrt{2}} = \dfrac{\sqrt{(\sqrt{5})^2 - 2.\sqrt{5}.\sqrt{3} + (\sqrt{3})^2}}{\sqrt{2}}$
$= \dfrac{\sqrt{(\sqrt{5} - \sqrt{3})^2}}{\sqrt{2}}$ $= \dfrac{|\sqrt{5} - \sqrt{3}|}{\sqrt{2}} = \dfrac{\sqrt{5} - \sqrt{3}}{\sqrt{2}}$
$= \dfrac{\sqrt{2}(\sqrt{5} - \sqrt{3})}{\sqrt{2}.\sqrt{2}} = \dfrac{\sqrt{10} - \sqrt{6}}{2}$
