Đáp án+Giải thích các bước giải:
`A = 4\sqrt{20} + 2\sqrt{45} - 8\sqrt{5} + 2\sqrt{180}`
`= 4\sqrt{4.5} + 2\sqrt{9.5} - 8\sqrt{5} + 2\sqrt{36.5}`
`= 8\sqrt{5} + 6\sqrt{5} - 8\sqrt{5} + 12\sqrt{5}`
`= 18\sqrt{5}`
`B = \frac{1}{\sqrt{5} + \sqrt{7}} - \frac{1}{\sqrt{5} - \sqrt{7}}`
`= \frac{1}{\sqrt{7} + \sqrt{5}} + \frac{1}{\sqrt{7} - \sqrt{5}}`
`= \frac{\sqrt{7} - \sqrt{5} + \sqrt{7} + \sqrt{5}}{(\sqrt{7} + \sqrt{5})(\sqrt{7} - \sqrt{5})}`
`= \frac{2\sqrt{7}}{7 - 5}`
`= \frac{2\sqrt{7}}{2}`
`= \sqrt{7}`
`C = \sqrt{\frac{4 + \sqrt{7}}{4 - \sqrt{7}}} + \sqrt{\frac{4 - \sqrt{7}}{4 + \sqrt{7}}}`
`= \sqrt{\frac{(4 + \sqrt{7})²}{(4 - \sqrt{7})(4 + \sqrt{7})}} + \sqrt{\frac{(4 - \sqrt{7})²}{(4 - \sqrt{7}).(4 + \sqrt{7})}}`
`= \sqrt{\frac{(4 + \sqrt{7})²}{16 - 7}} + \sqrt{\frac{(4 - \sqrt{7})²}{16 - 7}}`
`= \frac{4 + \sqrt{7}}{3} + \frac{4 - \sqrt{7}}{3}`
`= \frac{4 + \sqrt{7} + 4 - \sqrt{7}}{3}`
`= \frac{8}{3}`
`D = \sqrt{5 + \sqrt{21}} + \sqrt{5 - \sqrt{21}}`
`⇒ \sqrt{2}D = \sqrt{2}(\sqrt{5 + \sqrt{21}} + \sqrt{5 - \sqrt{21}})`
`= \sqrt{10 + 2\sqrt{21}} + \sqrt{10 - 2\sqrt{21}}`
`= \sqrt{(\sqrt{7} + \sqrt{3})²} + \sqrt{(\sqrt{7} - \sqrt{3})²}`
`= \sqrt{7} + \sqrt{3} + \sqrt{7} - \sqrt{3}`
`= 2\sqrt{7}`
`⇒ D = \sqrt{14}`
