Verified answer

[tex] \sqrt{ {(6 \sqrt{3} - 11)}^{2} } + 6 \sqrt{3} =- 6 \sqrt{3 } + 11 + 6 \sqrt{3} = 11[/tex]

[tex]\sqrt{(6\sqrt{3}- 11)^2} +6\sqrt{3} =|6\sqrt{3}-11|+6\sqrt{3} =-( 6\sqrt{3}-11)+6\sqrt{3}=-6\sqrt{3}+11+6\sqrt{3}=11[/tex]