$\displaystyle \begin{array}{{>{\displaystyle}l}} Bài\ 3:\ \\ a)\sqrt{9( x-5)^{2}} =3|x-5|=3x-15( \ x\geqslant 5) \ \\ b) \ \sqrt{x^{2}( x-2)^{2}} =|x|.|x-2|=x( x-2) =x^{2} -2x\ \\ Vì\ x< 0\ \rightarrow x< 2\ \\ d)\frac{\sqrt{108x^{3}}}{\sqrt{12x}} =\sqrt{\frac{108x^{3}}{12x}} =\sqrt{9x^{2}} =3|x|=3x( \ x >0) \ \\ d)\frac{\sqrt{13x^{4} y^{6}}}{\sqrt{208x^{6} y^{6}}} \ =\sqrt{\frac{13x^{4} y^{6}}{208x^{6} y^{6}}} =\sqrt{\frac{1}{16x^{2}}} =\frac{1}{4|x|} =\frac{-1}{4x} \ ( x< 0)\\ Bài\ 4:\ \\ a) \ \sqrt{6+\sqrt{35}} .\sqrt{6-\sqrt{35}} =\sqrt{\left( 6+\sqrt{35}\right)\left( 6-\sqrt{35}\right)}\\ =\sqrt{36-35} =\sqrt{1} =1\ \\ b)\sqrt{9-\sqrt{17}} .\sqrt{9+\sqrt{17}} =\sqrt{\left( 9-\sqrt{17}\right)\left( 9+\sqrt{17}\right)}\\ =\sqrt{81-17} =\sqrt{64} =8\ \\ c) \ \left(\sqrt{2} -1\right)^{2} =\sqrt{9} -\sqrt{8} \ \\ Ta\ có\ :\ \sqrt{9} -\sqrt{8} =3-2\sqrt{2} =1-2\sqrt{2} +2\ \\ =\left(\sqrt{2} -1\right)^{2} =VT\ \\ d) \ \left(\sqrt{4} -\sqrt{3}\right)^{2} =\sqrt{49} -\sqrt{48} \ \\ Ta\ có\ :\ \sqrt{49} -\sqrt{48} =7-4\sqrt{3} \ =4-2.2\sqrt{3} +3\\ =\left( 2-\sqrt{3}\right)^{2} =\left(\sqrt{4} -\sqrt{3}\right)^{2} =VT\ \\ e) \ 2\sqrt{2}\left( 2-3\sqrt{3}\right) +\left( 1-2\sqrt{2}\right)^{2} +6\sqrt{6}\\ =4\sqrt{2} -6\sqrt{6} +1-4\sqrt{2} +8+6\sqrt{6} \ \\ =9\\ \ \\ \end{array}$
