`#tnvt`
`\sqrt{5+\sqrt{24}}+\sqrt{5-\sqrt{24}}`
`=\frac{\sqrt{2}.(\sqrt{5+\sqrt{24}}+\sqrt{5-\sqrt{24}})}{\sqrt{2}}`
`=\frac{\sqrt{10+2\sqrt{24}}+\sqrt{10-2\sqrt{24}}}{\sqrt{2}}`
`=\frac{\sqrt{6+2.\sqrt{6}.\sqrt{4}+4}+\sqrt{6-2.\sqrt{6}.\sqrt{4}+4}}{\sqrt{2}}`
`=\frac{\sqrt{(\sqrt{6}+\sqrt{4})^2}+\sqrt{(\sqrt{6}-\sqrt{4})^2}}{\sqrt{2}}`
`=\frac{|\sqrt{6}+\sqrt{4}|+|\sqrt{6}-\sqrt{4}|}{\sqrt{2}}`
`=\frac{\sqrt{6}+\sqrt{4}+\sqrt{6}-\sqrt{4}}{\sqrt{2}}`
`=\frac{2\sqrt{6}}{\sqrt{2}}`
`=\frac{2\sqrt{3}.\sqrt{2}}{\sqrt{2}}`
