a)\(\left(\sqrt{12}+2\sqrt{27}\right)\frac{\sqrt{3}}{2}-\sqrt{150}\)
b)\(\left(\sqrt{28}-\sqrt{12}-\sqrt{7}\right).\sqrt{7}+2\sqrt{21}\)
c)\(\left(1+\sqrt{2}-\sqrt{3}\right).\left(1+\sqrt{2}+\sqrt{3}\right)\)
d)\(\sqrt{3}.\left(\sqrt{2}-\sqrt{3}\right)^2-\left(\sqrt{3}-\sqrt{2}\right)\)
thực hiện phép tính
a, \(\frac{\left(\sqrt{12}+2\sqrt{27}\right)\sqrt{3}}{2}-\sqrt{150}\)
\(=\frac{\left(2\sqrt{3}+6\sqrt{3}\right)\sqrt{3}}{2}-5\sqrt{6}=\frac{24}{2}-5\sqrt{6}=12-5\sqrt{6}\)
b, \(\left(\sqrt{28}-\sqrt{12}-\sqrt{7}\right)\sqrt{7}+2\sqrt{21}\)
\(=\left(2\sqrt{7}-2\sqrt{3}-\sqrt{7}\right)\sqrt{7}+2\sqrt{21}\)
\(=\left(\sqrt{7}-2\sqrt{3}\right)\sqrt{7}+2\sqrt{21}=7-2\sqrt{21}+2\sqrt{21}=7\)
c, \(\left(1+\sqrt{2}-\sqrt{3}\right)\left(1+\sqrt{2}+\sqrt{3}\right)=\left(1+\sqrt{2}\right)^2-3\)
\(=3+2\sqrt{2}-3=2\sqrt{2}\)
d, \(\sqrt{3}\left(\sqrt{2}-\sqrt{3}\right)^2-\left(\sqrt{3}-\sqrt{2}\right)\)
\(=\left(\sqrt{3}-\sqrt{2}\right)\left[\sqrt{3}\left(\sqrt{3}-\sqrt{2}\right)-1\right]\)
\(=\left(\sqrt{3}-\sqrt{2}\right)\left(3-\sqrt{6}-1\right)=\left(\sqrt{3}-\sqrt{2}\right)\left(2-\sqrt{6}\right)\)
\(=-\sqrt{2}\left(\sqrt{3}-\sqrt{2}\right)^2=-\sqrt{2}\left(5-2\sqrt{6}\right)=-5\sqrt{2}+4\sqrt{3}\)