Question

Please help!! Thank you in advance !!! Simplify: 7√3 - 4√6 + √48 - √54

Answer 1

$\bf 7\sqrt{3}-4\sqrt{6}+\sqrt{48}-\sqrt{54}\\\\ -----------------------------\\\\ now\implies \begin{cases} 6\to 2\cdot 3\\\\ 48\to 2\cdot 2\cdot 2\cdot 2\cdot 3\\ \qquad 2^2\cdot 2^2\cdot 3\\ \qquad (2^2)^2\cdot 3\\\\ 54\to 2\cdot 3\cdot 3\cdot 3\\ \qquad 2\cdot 3^2\cdot 3 \end{cases}\\\\ -----------------------------\\\\ 7\sqrt{3}-4\sqrt{2\cdot 3}+\sqrt{(2^2)^2\cdot 3}-\sqrt{2\cdot 3^2\cdot 3} \\\\\\ 7\sqrt{3}-4\sqrt{6}+4\sqrt{3}-3\sqrt{6}$

$\bf \boxed{7\sqrt{3}+4\sqrt{3}}\quad \boxed{-4\sqrt{6}-3\sqrt{6} }$

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