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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]
=53+548−10(2+3)=\sqrt{5 \sqrt{3}+5\sqrt{48-10(2+\sqrt{3})}}
=53+528−103=\sqrt{5 \sqrt{3}+5\sqrt{28-10\sqrt{3}}}
=53+5(5−3)2=\sqrt{5 \sqrt{3}+5 \sqrt{(5-\sqrt{3})^2}}
=53+25−53=\sqrt{5 \sqrt{3}+25-5\sqrt{3}}
=5=5
 
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