1: =3-căn 2-3-căn 2=-2căn 2
2: \(=\sqrt{5}-2+3-\sqrt{5}=1\)
3: \(=\left(\sqrt{7}+2\right)\left(\sqrt{7}-2\right)=7-4=3\)
4: \(=3+\sqrt{2}+2-\sqrt{2}=5\)
6: \(=\dfrac{2\sqrt{2}-\sqrt{6}}{2+\sqrt{3}+1}+\dfrac{2\sqrt{2}+\sqrt{6}}{2-\sqrt{3}+1}\)
\(=\dfrac{2\sqrt{2}-\sqrt{6}}{3+\sqrt{3}}+\dfrac{2\sqrt{2}+\sqrt{6}}{3-\sqrt{3}}\)
\(=\dfrac{\sqrt{2}\left(2-\sqrt{3}\right)\left(3-\sqrt{3}\right)+\sqrt{2}\left(2+\sqrt{3}\right)\left(3+\sqrt{3}\right)}{9-3}\)
\(=\dfrac{\sqrt{2}\left(6-5\sqrt{3}+3\right)+\sqrt{2}\left(9+5\sqrt{3}\right)}{6}\)
\(=\dfrac{\sqrt{2}\cdot18}{6}=3\sqrt{2}\)
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