Question

A=\(\sqrt{12-6\sqrt{3}}-\sqrt{21-12\sqrt{3}}\)

Answer 1

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

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

Answer 2

`A=\sqrt{12-6\sqrt{3}}-\sqrt{21-12\sqrt{3}}`

`A=\sqrt{(\sqrt{3})^2-2.\sqrt{3}.2+3^2}-\sqrt{3^2-2.3.2\sqrt{3}+(2\sqrt{3})^2}`

`A=\sqrt{(\sqrt{3}-3)^2}-\sqrt{(3-2\sqrt{3})^2}`

`A=|\sqrt{3}-3|-|3-2\sqrt{3}|`

`A=(3-\sqrt{3})-(2\sqrt{3}-3)`

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

`A=6-3\sqrt{3}`