3/2 √6+2√(2/3)-√(3/2)

`3/2\sqrt{6}+2\sqrt{2/3}-\sqrt{3/2}`

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

`=(3\sqrt{6})/(2)+(2\sqrt{2}.\sqrt{3})/(\sqrt{3}.\sqrt{3})-(\sqrt{3}.\sqrt{2})/(\sqrt{2}.\sqrt{2})`

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

`=3/2\sqrt{6}+2/3\sqrt{6}-1/2\sqrt{6}`

`=\sqrt{6}.(3/2+2/3-1/2)`

`=\sqrt{6}.(1+2/3)`

`=\sqrt{6}.(3/3+2/6)`

`=\sqrt{6}.(5)/3`

`=(5\sqrt{6})/3`

Đáp án+Giải thích các bước giải:

`\frac{3}{2}\sqrt{6}+2\sqrt{\frac{2}{3}}-\sqrt{\frac{3}{2}}`

`=\frac{3\sqrt{6}}{2}+2.\frac{\sqrt{2}}{\sqrt{3}}-\frac{\sqrt{3}}{\sqrt{2}}`

`=\frac{3\sqrt{6}}{2}+\frac{2.\sqrt{2}.\sqrt{3}}{\sqrt{3}.\sqrt{3}}-\frac{\sqrt{3}.\sqrt{2}}{\sqrt{2}.\sqrt{2}}`

`=\frac{3\sqrt{6}}{2}+\frac{2\sqrt{6}}{3}-\frac{\sqrt{6}}{2}`

`=\frac{9\sqrt{6}+4\sqrt{6}-3\sqrt{6}}{6}`

`=\frac{10\sqrt{6}}{6}`

`=\frac{5\sqrt{6}}{3}`