Question

\(\left(\dfrac{3}{2}\sqrt{6\:\:}+\:2\sqrt{\dfrac{2}{3}\:\:\:\:\:\:\:\:\:}-4\sqrt{\dfrac{3}{2}}\right)\left(3\sqrt{\dfrac{2}{3}}-\sqrt{12}-\sqrt{6}\right)\)

Answer 1

\(\left(\dfrac{3}{3}\sqrt{6}+2\sqrt{\dfrac{2}{3}}-4\sqrt{\dfrac{3}{2}}\right)\left(3\sqrt{\dfrac{2}{3}}-\sqrt{12}-\sqrt{6}\right)\)

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

=\(\text{[}\sqrt{6}\left(\dfrac{3}{2}+\dfrac{2}{3}-2\right)\text{]}.\left(-2\sqrt{3}\right)\)

=\(\dfrac{1}{6}\sqrt{6}.\left(-2\sqrt{3}\right)=-\sqrt{2}\)