what is the simplified form of the following expression?\n2\\sqrt{27}+\\sqrt{12}-3\\sqrt{3}-2\\sqrt{12}\n\\(\…

Explanation:

Step1: Simplify square - root terms

Simplify $\sqrt{27}=\sqrt{9\times3}=3\sqrt{3}$ and $\sqrt{12}=\sqrt{4\times3}=2\sqrt{3}$. The original expression $2\sqrt{27}+\sqrt{12}-3\sqrt{3}-2\sqrt{12}$ becomes $2\times3\sqrt{3}+2\sqrt{3}-3\sqrt{3}-2\times2\sqrt{3}$.

Step2: Calculate the coefficients of $\sqrt{3}$

$2\times3\sqrt{3}+2\sqrt{3}-3\sqrt{3}-2\times2\sqrt{3}=6\sqrt{3}+2\sqrt{3}-3\sqrt{3}-4\sqrt{3}$.

Step3: Combine like - terms

$(6 + 2-3 - 4)\sqrt{3}=(8 - 3-4)\sqrt{3}=(5 - 4)\sqrt{3}=\sqrt{3}$.

Answer:

$\sqrt{3}$