Question

c/m:

\(\sqrt{21-6\sqrt{6}}+\sqrt{9+2\sqrt{18}}-2\sqrt{6+3\sqrt{3}}=0\)

Answer 1

`VT=\sqrt{21-6\sqrt{6}}+\sqrt{9+2\sqrt{18}}-2\sqrt{6+3\sqrt{3}}`

    `=\sqrt{(3\sqrt{2}-\sqrt{3})^2}+\sqrt{(\sqrt{6}+\sqt{3})^2}-\sqrt{24+12\sqrt{3}}`

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

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

    `=0=VP`

`=>Đpcm`

Answer 2

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

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

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

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