Question

\(\sqrt{33-12\sqrt{6}}\) - \(\sqrt{\left(1-\sqrt{6}\right)^2}\)

 

Answer 1

\(\sqrt{33-12\sqrt{6}}-\sqrt{\left(1-\sqrt{6}\right)^2}\)

\(=\sqrt{24-2\cdot2\sqrt{6}\cdot3+9}-\left(\sqrt{6}-1\right)\)

\(=\sqrt{\left(2\sqrt{6}-3\right)^2}-\left(\sqrt{6}-1\right)\)

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

Answer 2

`sqrt{33 - 12sqrt{6}} - sqrt{(1-sqrt{6})^2}`

`= sqrt{33 -  2.2sqrt{6}.3} - |1-sqrt{6}|`

`= sqrt{(2sqrt{6})^2 -  2.2sqrt{6}.3 + 3^2} - (sqrt{6} - 1)`

`= sqrt{(2sqrt{6}- 3)^2} - (sqrt{6} - 1)`

`= |2sqrt{6}- 3| - sqrt{6} + 1`

`= 2sqrt{6}- 3 - sqrt{6} + 1`

`= sqrt{6} - 2`