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