Question

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A= \(2\sqrt{27}-\sqrt{\left(1-\sqrt{3}\right)^2}+\dfrac{1}{2-\sqrt{3}}\)

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Answer 1

\(A=2\sqrt{27}-\sqrt{\left(1-\sqrt{3}\right)^2}+\dfrac{1}{2-\sqrt{3}}\\ =2.3\sqrt{3}-\left|1-\sqrt{3}\right|+\dfrac{2+\sqrt{3}}{\left(2-\sqrt{3}\right)\left(2+\sqrt{3}\right)}\\ =6\sqrt{3}-\left(-1+\sqrt{3}\right)+\dfrac{2+\sqrt{3}}{2^2-\sqrt{3^2}}\\ =6\sqrt{3}+1-\sqrt{3}+2+\sqrt{3}\\ =6\sqrt{3}+3\)

Answer 2

\(=6\sqrt{3}-\sqrt{3}+1+2+\sqrt{3}=6\sqrt{3}+3\)