1: \(=4\sqrt{3}-10\sqrt{3}+6\sqrt{3}-\sqrt{3}=-\sqrt{3}\)
2: =3*căn 11*căn 11=33
3: \(=2\sqrt{6}-\sqrt{6}-\sqrt{6}=0\)
4:
=3-căn 2-3-căn 2
=-2*căn 2
\(1,\sqrt{48}-2\sqrt{75}+\sqrt{108}-\dfrac{1}{7}\sqrt{147}=\sqrt{4^2.3}-2\sqrt{5^2.3}+\sqrt{6^2.3}-\dfrac{1}{7}\sqrt{7^2.3}\)
\(=4\sqrt{3}-2.5\sqrt{3}+6\sqrt{3}-\dfrac{1}{7}.7\sqrt{3}\)
\(=4\sqrt{3}-10\sqrt{3}+6\sqrt{3}-\sqrt{3}\)
\(=\sqrt{3}.\left(4-10+6-1\right)\)
\(=-\sqrt{3}\)
\(2,\left(\sqrt{44}+\sqrt{11}\right)\sqrt{11}=\left(\sqrt{2^2.11}+\sqrt{11}\right)\sqrt{11}=\left(2\sqrt{11}+\sqrt{11}\right)\sqrt{11}=3\sqrt{11}.\sqrt{11}=3.\sqrt{11^2}=3.11=33\)
\(3,\sqrt{24}-6\sqrt{\dfrac{1}{6}}-\dfrac{3\sqrt{2}}{\sqrt{3}}=\sqrt{2^2.6}-6.\dfrac{\sqrt{6}}{6}-\dfrac{\sqrt{3^2.2}}{\sqrt{3}}=2\sqrt{6}-\sqrt{6}-\sqrt{\dfrac{3^2.2}{3}}=\sqrt{6}-\sqrt{6}=0\)
\(4,\sqrt{11-6\sqrt{2}}-\sqrt{11+6\sqrt{2}}=\sqrt{\left(3-\sqrt{2}\right)^2}-\sqrt{\left(3+\sqrt{2}\right)^2}\)
\(=3-\sqrt{2}-3-\sqrt{2}\)
\(=-2\sqrt{2}\)
\(5,\sqrt{\left(2-\sqrt{5}\right)^2}+\sqrt{14-6\sqrt{5}}=\left|2-\sqrt{5}\right|+\sqrt{\left(3-\sqrt{5}\right)^2}=-2+\sqrt{5}+3-\sqrt{5}=1\)
\(6,\left(2+\sqrt{7}\right)\sqrt{11-4\sqrt{7}}=\left(2+\sqrt{7}\right)\sqrt{\left(\sqrt{7}-2\right)}^2=\left(2+\sqrt{7}\right)\left(\sqrt{7}-2\right)=\sqrt{7^2}-2^2=7-4=3\)
\(7,\sqrt{\left(3+\sqrt{2}\right)^2}+\sqrt{6-4\sqrt{2}}=3+\sqrt{2}+\sqrt{\left(2-\sqrt{2}\right)^2}=3+\sqrt{2}+2-\sqrt{2}=5\)
