[tex] \sqrt{21-12 \sqrt{3} } + \sqrt{21+12 \sqrt{3} } =[/tex]

[tex]\sqrt{21-12\sqrt3}+\sqrt{21+12\sqrt3}=\sqrt{(3-2\sqrt3)^2}+\sqrt{(3+2\sqrt3)^2}= \\ =|3-2\sqrt3|+|3+2\sqrt3|=2\sqrt3-3+3+2\sqrt3=4\sqrt3[/tex]