Question

sqrt(12-6*sqrt(3))+sqrt(4-2*sprt(3)

Answer 1

4-2sqrt(3)=(sqrt(3)-1)^2

12-6sqrt(3)=(3-sqrt(3))^2

sqrt(3)-1+3-sqrt(3)=2

Answer 2

$sqrt{12-6sqrt{3}}+sqrt{4-2sqrt{3}}=\\sqrt{9-6sqrt{3}+3}+sqrt{3-2sqrt{3}+1}=\\sqrt{3^2-2*3*sqrt{3}+(sqrt{3})^2}+sqrt{(sqrt{3})^2-2*sqrt{3}*1+1^2}=\\sqrt{(3-sqrt{3})^2}+sqrt{(sqrt{3}-1)^2}=\\|3-sqrt{3}|+|sqrt{3}-1|=3-sqrt{3}+sqrt{3}-1=2$