a) $\sqrt{24+8\sqrt{5}}+\sqrt{9-4\sqrt{5}}$
$=\sqrt{2+2.2.2\sqrt{5}+(2\sqrt{5})^2}+\sqrt{5-2.2\sqrt{5}+4}$
$=\sqrt{(2+2\sqrt{5})^2}+\sqrt{(\sqrt{5}-2)^2}$
$=2+2\sqrt{5}+\sqrt{5}-2$
$=3\sqrt{5}$
b) $\sqrt{6-4\sqrt{2}}+\sqrt{22-12\sqrt{2}}$
$=\sqrt{(2-\sqrt{2})^2}+\sqrt{(3\sqrt{2}-2)^2}$
$=2-\sqrt{2}+3\sqrt{2}-2$
$=2\sqrt{2}$
c) Để biểu thức $\dfrac{1}{\sqrt{x+2\sqrt{x-1}}}$ có nghĩa
$⇔x+2\sqrt{x-1}\neq0$
$x-1≥0$
$⇔x\neq2\sqrt{x-1}$
$x≥1$