a. $\dfrac{3}{\sqrt{5} + \sqrt{2}} + \sqrt{7 + 2\sqrt{10}}$
$= \dfrac{3(\sqrt{5} - \sqrt{2})}{(\sqrt{5} + \sqrt{2})(\sqrt{5} - \sqrt{2})}$ $ + \sqrt{(\sqrt{5})^2 + 2.\sqrt{5}.\sqrt{2} + (\sqrt{2})^2}$
$= \dfrac{3(\sqrt{5} - \sqrt{2})}{5 - 2} + \sqrt{(\sqrt{5} + \sqrt{2})^2}$
$= \sqrt{5} - \sqrt{2} + \sqrt{5} + \sqrt{2} = 2\sqrt{5}$
b. $\sqrt{19 - 8\sqrt{3}} + \sqrt{3} = $
$= \sqrt{(4 - \sqrt{3})^2} + \sqrt{3}$
$= 4 - \sqrt{3} + \sqrt{3} = 4$
c. $\sqrt{13 - 4\sqrt{3}} + \sqrt{3} - \sqrt{27}$
$= \sqrt{(2\sqrt{3} - 1)^2} + \sqrt{3} - \sqrt{9.3}$
$= 2\sqrt{3} - 1 + \sqrt{3} - 3\sqrt{3} = - 1$
d. $\sqrt{2\sqrt{6} + 7} - \sqrt{(\sqrt{6} - 1)^2}$
$= \sqrt{\sqrt{6} + 1)^2} - \sqrt{(\sqrt{6} - 1)^2}$
$= \sqrt{6} + 1 - (\sqrt{6} - 1) =$
$= \sqrt{6} + 1 - \sqrt{6} + 1 = 2$
