[tex] \sqrt{21- 12\sqrt{3} }=? \\
Facem~formula~(a-b)^2=a^2+b^2-2ab,~unde: \\
a^2+b^2=21 \\
2ab=12 \sqrt{3}=>ab=6 \sqrt{3} \left \{ {{a=2 \sqrt{3};~a^2=12 } \atop {b=3~~~~~;~b^2=9}} \right. \\
\sqrt{21- 12\sqrt{3} }= \sqrt{(2 \sqrt{3}-3)^2 }=|2 \sqrt{3}-3 | = 2\sqrt{3}-3 [/tex]
