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[TEX]\sqrt{5 \sqrt{3}+5\sqrt{48-10\sqrt{7+4\sqrt{3}}}}[/TEX]
[TEX]=\sqrt{5 \sqrt{3}+5\sqrt{48-10\sqrt{(2+\sqrt{3})^2}}}[/TEX]
[tex]=\sqrt{5 \sqrt{3}+5\sqrt{48-10(2+\sqrt{3})}}[/tex]
[tex]=\sqrt{5 \sqrt{3}+5\sqrt{28-10\sqrt{3}}}[/tex]
[tex]=\sqrt{5 \sqrt{3}+5 \sqrt{(5-\sqrt{3})^2}}[/tex]
[tex]=\sqrt{5 \sqrt{3}+25-5\sqrt{3}}[/tex]
[tex]=5[/tex]
 
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