15. Đặt:
$t = \sqrt{7 + 4\sqrt{3}} + \sqrt{7 - 4\sqrt{3}}$
$t^2 = (\sqrt{7 + 4\sqrt{3}} + \sqrt{7 - 4\sqrt{3}})^2 =$
$= 7 + 4\sqrt{3} + 7 - 4\sqrt{3} + 2\sqrt{(7 + 4\sqrt{3})(7 - \sqrt{3})}$
$= 14 + 2\sqrt{49 - 48}$
$= 14 + 2 = 16$
Suy ra: $t = \sqrt{t^2} = \sqrt{16} = 4$
16. Đặt
$a = \sqrt{9 - 2\sqrt{14}} + \sqrt{9 - 2\sqrt{14}}$
Ta có:
$\sqrt{9 - 2.\sqrt{14}} =$$ \sqrt{(\sqrt{7})^2 - 2.\sqrt{7}.\sqrt{2} + (\sqrt{2})^2}$
$= \sqrt{(\sqrt{7} - \sqrt{2})^2} = \sqrt{7} - \sqrt{2}$
Vậy $a = 2.(\sqrt{7} - \sqrt{2})$
