a: \(P=\left(2+3\sqrt{2}\right)\cdot\left(1-\sqrt{2}\left(3-\sqrt{2}\right)\right)\)
\(=\left(3\sqrt{2}+2\right)\left(1-3\sqrt{2}+2\right)\)
\(=\left(3\sqrt{2}+2\right)\left(-3\sqrt{2}+3\right)\)
\(=-18+9\sqrt{2}-6\sqrt{2}+6=-12+3\sqrt{2}\)
b: \(P=\sqrt{3}+1+4+\sqrt{3}=5+2\sqrt{3}\)
c: \(C=\left(\dfrac{\sqrt{3}\left(\sqrt{3}+\sqrt{2}\right)}{\sqrt{4}\left(\sqrt{3}+\sqrt{2}\right)}+\dfrac{3\sqrt{3}}{6}\right)\cdot\dfrac{1}{\sqrt{3}}\)
\(=\left(\dfrac{\sqrt{3}}{2}+\dfrac{\sqrt{3}}{2}\right)\cdot\dfrac{1}{\sqrt{3}}=\dfrac{2\sqrt{3}}{2}\cdot\dfrac{1}{\sqrt{3}}=1\)
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