`B=\sqrt{9+4\sqrt{5}}+\sqrt{9-4\sqrt{5}}`
`=\sqrt{5+4\sqrt{5}+4}+\sqrt{5-4\sqrt{5}+4}`
`=\sqrt{(\sqrt{5}+2)^2}+\sqrt{(\sqrt{5}-2)^2}`
`=|\sqrt{5}+2|+|\sqrt{5}-2|`
`=\sqrt{5}+2+\sqrt{5}-2`
`=2\sqrt{5}`
`C=\sqrt{5+2\sqrt{6}}+\sqrt{5-2\sqrt{6}}`
`=\sqrt{3+2\sqrt{6}+2}+\sqrt{3-2\sqrt{6}+2}`
`=\sqrt{(\sqrt{3}+\sqrt{2})^2}+\sqrt{(\sqrt{3}-\sqrt{2})^2}`
`=|\sqrt{3}+\sqrt{2}|+|\sqrt{3}-\sqrt{2}|`
`=\sqrt{3}+\sqrt{2}+\sqrt{3}-\sqrt{2}`
`=2\sqrt{3}`
`D=\frac{1}{\sqrt{3}-\sqrt{5}}-\frac{1}{\sqrt{3}+\sqrt{5}}`
`=\frac{\sqrt{3}+\sqrt{5}-\sqrt{3}+\sqrt{5}}{(\sqrt{3}-\sqrt{5})(\sqrt{3}+\sqrt{5})}`
`=\frac{2\sqrt{5}}{3-5}`
`=\frac{2\sqrt{5}}{-2}`
`=-\sqrt{5}`
