Ta có
$A = \sqrt{7 - \sqrt{13}} + \sqrt{7 - \sqrt{13}}$
$= 2\sqrt{7 - \sqrt{13}}$
$= \sqrt{2} . \sqrt{14 - 2\sqrt{13}}$
$= \sqrt{2} . \sqrt{13 - 2.1.\sqrt{13} + 1}$
$= \sqrt{2} . \sqrt{(\sqrt{13} - 1)^2}$
$= \sqrt{2} (\sqrt{13} - 1)$
$= \sqrt{26} - \sqrt{2}$
Vậy $A = \sqrt{26} - \sqrt{2}$.