Question

CMR : 3/2 *căn 6+2* căn 2/3 -4* căn 3/2 =căn 6/6

Answer 1

\(\frac{3}{2}\sqrt{6}+2\sqrt{\frac{2}{3}}-4\sqrt{\frac{3}{2}}\)

\(=\frac{3}{2}\sqrt{6}+2.\frac{\sqrt{2}}{\sqrt{3}}-4.\frac{\sqrt{3}}{\sqrt{2}}\)

\(=\frac{3\sqrt{6}}{2}+2.\frac{\sqrt{2}}{\sqrt{3}}-4.\frac{\sqrt{3}}{\sqrt{2}}\)

\(=\frac{3\sqrt{6}}{2}+\frac{2\sqrt{2}.\sqrt{3}}{3}-\frac{4\sqrt{3}.\sqrt{2}}{2}\)

\(=\frac{3\sqrt{6}}{2}+\frac{2\sqrt{6}}{3}-\frac{4\sqrt{6}}{2}\)

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

\(=\frac{\sqrt{6}}{6}\)