Question

Answer 1

\(a,\sqrt{9-4\sqrt{5}}-\sqrt{5}=\sqrt{\left(\sqrt{5}-2\right)^2}-\sqrt{5}\\ =\sqrt{5}-2-\sqrt{5}=-2\\ b,\dfrac{3}{2}\sqrt{6}+2\sqrt{\dfrac{2}{3}}-4\sqrt{\dfrac{3}{2}}\\ =\dfrac{3\sqrt{6}}{2}+\dfrac{2\sqrt{6}}{3}-2\sqrt{6}\\ =\dfrac{9\sqrt{6}+4\sqrt{6}-12\sqrt{6}}{6}=\dfrac{\sqrt{6}}{6}\\ c,2\sqrt{2}\left(\sqrt{3}-2\right)+\left(1+2\sqrt{2}\right)^2-2\sqrt{6}\\ =2\sqrt{6}-4\sqrt{2}+9+4\sqrt{2}-2\sqrt{6}\\ =9\)