Question

Answer 1

\(3,\dfrac{3}{2}\sqrt{6}+2\sqrt{\dfrac{2}{3}}-4\sqrt{\dfrac{3}{2}}\\ =\sqrt{\dfrac{9}{4}.6}+\sqrt{4.\dfrac{2}{3}}-\sqrt{16.\dfrac{3}{2}}\\ =\sqrt{\dfrac{27}{2}}+\sqrt{\dfrac{8}{3}}-\sqrt{24}\\ =\dfrac{3\sqrt{6}}{2}+\dfrac{2\sqrt{6}}{3}-2\sqrt{6}\\ =\dfrac{9\sqrt{6}+4\sqrt{6}-12\sqrt{6}}{6}=\dfrac{\sqrt{6}}{6}\)

\(4,5\sqrt{x}+6\sqrt{\dfrac{x}{4}}-x\sqrt{\dfrac{4}{x}}\\ =5\sqrt{x}+\sqrt{\dfrac{36x}{4}}-\sqrt{\dfrac{4x^2}{x}}\\ =5\sqrt{x}+\sqrt{9x}-\sqrt{4x}\\ =5\sqrt{x}+3\sqrt{x}-2\sqrt{x}\\ =6\sqrt{x}\)