Question

Rút gọn

B = \(\left(3\sqrt{2}+\sqrt{6}\right)\sqrt{6-3\sqrt{3}}\)

Answer 1

B=\(\dfrac{\left(3\sqrt{2}+\sqrt{6}\right)\sqrt{12-6\sqrt{3}}}{\sqrt{2}}\)

=(3+\(\sqrt{3}\))\(\sqrt{9-6\sqrt{3}+3}\)

=(3+\(\sqrt{3}\))\(\sqrt{\left(3-\sqrt{3}\right)^2}\)

=(3+\(\sqrt{3}\))(3-\(\sqrt{3}\))=9-3=6

Answer 2

B=(\(3\sqrt{2}+\sqrt{6}\))\(\sqrt{6-3\sqrt{3}}\)

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

= \(\left(3+\sqrt{3}\right)\sqrt{12-6\sqrt{3}}\)

= \(\left(3+\sqrt{3}\right)\sqrt{9-2\cdot3\cdot\sqrt{3}+3}\)

=\(\left(3+\sqrt{3}\right)\sqrt{\left(3-\sqrt{3}\right)^2}\)

=\(\left(3+\sqrt{3}\right)\left|3-\sqrt{3}\right|\)

= \(\left(3+\sqrt{3}\right)\left(3-\sqrt{3}\right)=3^2-\left(\sqrt{3}\right)^2=9-3=6\)