Tính giá trị biểu thức $A=\sqrt{6-2\sqrt{5}}+\sqrt{14-6\sqrt{5}}$.

minhthu_

$A=\sqrt{6-2\sqrt{5}}+\sqrt{14-6\sqrt{5}}$

$=\sqrt{\left(\sqrt{5}\right)^2-2\sqrt{5}.1+1^2}+\sqrt{3^2-2.3.\sqrt{5}+\left(\sqrt{5}\right)^2}$

$=\sqrt{\left(\sqrt{5}-1\right)^2}+\sqrt{\left(3-\sqrt{5}\right)^2}$

$=\left|\sqrt{5}-1\right|+\left|3-\sqrt{5}\right|$

$=\sqrt{5}-1+3-\sqrt{5}$

$=2$.