$1)$
$a) \sqrt{125} + \frac{1}{4}\sqrt{80} - 2\sqrt{45}$
$= 5\sqrt{5} +\frac{1}{4}.4\sqrt{5} - 2.5.\sqrt{9}$
$ = 5\sqrt{5} + \sqrt{5} - 10.3$
$ = 6\sqrt{5} - 30$
$b) \sqrt{3+2\sqrt{2}} - \sqrt{9+4\sqrt{2}}$
$= \sqrt{2+2\sqrt{2}+1} - \sqrt{8+4\sqrt{2}+1}$
$= \sqrt{(\sqrt{2}+1)^2} - \sqrt{(\sqrt{8}+1)^2}$
$= (\sqrt{2} + 1) - (\sqrt{8} + 1)$
$= \sqrt{2} - \sqrt{8}$
$2)$
$\sqrt{9x^2+6x+1} = 3$
⇔ $\sqrt{(3x+1)^2} = 3$
⇔ $ |3x + 1| = 3 $
$TH1 : 3x + 1 = 3 $
$⇔ 3x = 2$
$⇔ x = \frac{2}{3}$
$TH2 : 3x + 1 = -3$
$⇔ 2x = -4$
$⇔ x = -2$
Vậy phương trình có tập nghiệm $S = {\frac{2}{3};-2}$
