a. $a = \sqrt{9 + 2\sqrt{14}} - \sqrt{9 - 2\sqrt{14}}$
$a^2 = 9 +2 \sqrt{14} + 9 - 2\sqrt{14} - 2\sqrt{(9 + 2\sqrt{14})(9 - 2\sqrt{14})}$
$a^2 = 18 - 2\sqrt{81 - 56} = 18 - 2\sqrt{25}$
$a^2 = 18 - 2.5 = 8$
Suy ra: $a = \sqrt{a^2} = \sqrt{8} = 2\sqrt{2}$
b. $b = \sqrt{15 - 6\sqrt{6}} + \sqrt{33 - 12\sqrt{6}}$
$b = \sqrt{(3 - \sqrt{6})^2} + \sqrt{(2\sqrt{6} - 3)^2}$
$= 3 - \sqrt{6} + 2\sqrt{6} - 3 = \sqrt{6}$
c. $c = \sqrt{7 + 4\sqrt{3}} + \sqrt{7 - 4\sqrt{3}}$
$c = \sqrt{(2 + \sqrt{3})^2} + \sqrt{(2 - \sqrt{3})^2}$
$c = 2 + \sqrt{3} + 2 - \sqrt{3} = 4$
d. $d = \sqrt{24 + 16\sqrt{2}} - \sqrt{24 - 16\sqrt{2}}$
$d = \sqrt{8(3 + 2\sqrt{2})} - \sqrt{8(3 - 2\sqrt{2})}$
$d = \sqrt{8}(\sqrt{3 + 2\sqrt{2}} - \sqrt{3 - 2\sqrt{2}}$
$d = \sqrt{8}(\sqrt{(\sqrt{2} + 1)^2} - \sqrt{(\sqrt{2} - 1)^2}$
$d = \sqrt{8}[\sqrt{2} + 1 - (\sqrt{2} - 1)]$
$= \sqrt{8}(\sqrt{2} + 1 - \sqrt{2} + 1)$
$= \sqrt{8}.2 = 4\sqrt{2}$
