Question

Rút gọn C= \(\left(3\sqrt{2}+\sqrt{6}\right)\sqrt{6-3\sqrt{3}}\)

Answer 1

\(C=\left(3+\sqrt{3}\right)\sqrt{2}.\sqrt{6-3\sqrt{3}}=\left(3+\sqrt{3}\right)\sqrt{9-2.3\sqrt{3}+3}=\left(3+\sqrt{3}\right)\left(3-\sqrt{3}\right)=6\)

Answer 2

\(C=\left(3\sqrt{2}+\sqrt{6}\right)\sqrt{6-3\sqrt{3}}\\ =\left[\sqrt{2}\left(3+\sqrt{3}\right)\right]\sqrt{6-3\sqrt{3}}\\ =\left(3+\sqrt{3}\right)\sqrt{12-6\sqrt{3}}\\ =\left(3+\sqrt{3}\right)\sqrt{9-2\cdot3\cdot\sqrt{3}+3}\\ =\left(3+\sqrt{3}\right)\sqrt{\left(3-\sqrt{3}\right)^2}\\ =\left(3+\sqrt{3}\right)\left(3-\sqrt{3}\right)\\ =3^3-\left(\sqrt{3}\right)^2\\ =9-3=6\)

Answer 3

@Phùng Khánh Linh