\(\sqrt{48-10\sqrt{7+4\sqrt{3}}+2+\sqrt{3}}\)
\(=\sqrt{48-10\sqrt{\left(2+\sqrt{3}\right)^2}}+2+\sqrt{3}\)
\(=\sqrt{48-20+10\sqrt{3}}+2+\sqrt{3}\)
\(=\sqrt{28-10\sqrt{3}}+2+\sqrt{3}\)
\(=\sqrt{\left(5-\sqrt{3}\right)^2}+2+\sqrt{3}\)
\(=5-\sqrt{3}+2+\sqrt{3}\)
\(=7\)
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\(\sqrt{48-10\sqrt{7+4\sqrt{3}}}+2+\sqrt{3}\)
\(=\sqrt{48-10\left(2+\sqrt{3}\right)}+2+\sqrt{3}\)
\(=5-\sqrt{3}+2+\sqrt{3}\)
=7
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