[tex]\sqrt{21-12\sqrt{3}}=\sqrt{21-\sqrt{432}} \\ \\ A=21 \\ B=432 \\ C^2=441-432=9 => \boxed{C=9} \\ \\ \sqrt{21-\sqrt{432}}=\sqrt{\frac{21+9}{2}-\sqrt{\frac{21-9}{2}}}= \sqrt{\frac{30}{2}-\sqrt{\frac{12}{2}}}= \\ \\ =\boxed{\sqrt{15}-\sqrt{6}}[/tex]
