a,
$\sqrt{\dfrac{4+2\sqrt3}{2}}-\sqrt{\dfrac{4-2\sqrt3}{2}}$
$=\sqrt{\dfrac{(\sqrt3+1)^2}{2}}-\sqrt{\dfrac{(\sqrt3-1)^2}{2}}$
$=\dfrac{\sqrt3+1-\sqrt3+1}{\sqrt2}$
$=\dfrac{2}{\sqrt2}=\sqrt2$
b,
$\sqrt{\dfrac{8-2\sqrt7}{2}}+\sqrt{\dfrac{8+2\sqrt7}{2}}$
$=\sqrt{\dfrac{(\sqrt7-1)^2}{2}}+\sqrt{\dfrac{(\sqrt7+1)^2}{2}}$
$=\dfrac{\sqrt7-1+\sqrt7+1}{\sqrt2}$
$=\dfrac{2\sqrt7}{\sqrt2}=\sqrt{14}$
c,
$\sqrt{\dfrac{6+2\sqrt5}{2}}+\sqrt{\dfrac{6-2\sqrt5}{2}}$
$=\sqrt{\dfrac{(\sqrt5+1)^2}{2}}+\sqrt{\dfrac{(\sqrt5-1)^2}{2}}$
$=\dfrac{\sqrt5+1+\sqrt5-1}{\sqrt2}$
$=\dfrac{2\sqrt5}{\sqrt2}=\sqrt{10}$
