a)(2+√3)√(7-4√3) b) √(2-√3) .(√6 +√2)

$\displaystyle \begin{array}{{>{\displaystyle}l}} a) \ \left( 2+\sqrt{3}\right)\sqrt{7-4\sqrt{3}}\\ =\left( 2+\sqrt{3}\right)\sqrt{4-2.2\sqrt{3} +3}\\ =\left( 2+\sqrt{3}\right)\sqrt{\left( 2-\sqrt{3}\right)^{2}}\\ =\left( 2+\sqrt{3}\right) |2-\sqrt{3} |\\ =\left( 2+\sqrt{3}\right)\left( 2-\sqrt{3}\right) \ \left( vì\ 2 >\sqrt{3}\right)\\ =4-3=1\\ b) \ \sqrt{2-\sqrt{3}} .\left(\sqrt{6} +\sqrt{2}\right)\\ =\sqrt{2-\sqrt{3}} .\sqrt{2}\left(\sqrt{3} +1\right)\\ =\sqrt{4-2\sqrt{3}} .\left(\sqrt{3} +1\right)\\ =\sqrt{1-2\sqrt{3} +3} .\left(\sqrt{3} +1\right)\\ =\sqrt{\left( 1-\sqrt{3}\right)^{2}} .\left(\sqrt{3} +1\right)\\ =|1-\sqrt{3} |.\left(\sqrt{3} +1\right)\\ =\left(\sqrt{3} -1\right)\left(\sqrt{3} +1\right) =3-1=2\ \left( vì\ \sqrt{3} >1\right) \ \\ \end{array}$