[tex]\bf 7\sqrt{3}-4\sqrt{6}+\sqrt{48}-\sqrt{54}\\\\
-----------------------------\\\\
now\implies
\begin{cases}
6\to 2\cdot 3\\\\
48\to 2\cdot 2\cdot 2\cdot 2\cdot 3\\
\qquad 2^2\cdot 2^2\cdot 3\\
\qquad (2^2)^2\cdot 3\\\\
54\to 2\cdot 3\cdot 3\cdot 3\\
\qquad 2\cdot 3^2\cdot 3
\end{cases}\\\\
-----------------------------\\\\
7\sqrt{3}-4\sqrt{2\cdot 3}+\sqrt{(2^2)^2\cdot 3}-\sqrt{2\cdot 3^2\cdot 3}
\\\\\\
7\sqrt{3}-4\sqrt{6}+4\sqrt{3}-3\sqrt{6}
\\\\\\
[/tex]
[tex]\bf \boxed{7\sqrt{3}+4\sqrt{3}}\quad \boxed{-4\sqrt{6}-3\sqrt{6}
}[/tex]
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