$\displaystyle \begin{array}{{>{\displaystyle}l}} a) \ \sqrt{7} .\sqrt{63}\\ =\sqrt{7.63} =\sqrt{7.7.9}\\ =\sqrt{7^{2}} .\sqrt{3^{2}}\\ =7.3=21\\ b)\sqrt{2,5} .\sqrt{30} .\sqrt{48}\\ =\sqrt{2,5.10.3.3.16}\\ =\sqrt{25} .\sqrt{9} .\sqrt{16}\\ =3.4.5\\ =60\ \\ c)\sqrt{1\frac{9}{16} .5\frac{4}{9} .0,01} \ \\ =\sqrt{\frac{25}{16} .\frac{49}{9} .0,01}\\ =\sqrt{\frac{25}{16}} .\sqrt{\frac{49}{9}} .\sqrt{0,01} \ \\ =\frac{5}{4} .\frac{7}{3} .\frac{1}{10} =\frac{7}{24} \ \\ d)\sqrt{\frac{149^{2} -76^{2}}{457^{2} -384^{2}}} =\sqrt{\frac{( 149+76)( 149-76)}{( 457-384)( 457+384)}}\\ =\sqrt{\frac{225.73}{73.841}} =\frac{15}{29} \ \\ Bài\ 2:\ \\ a) \ \sqrt{0,36x^{2}} .\ a< 0\ \\ =0,6|a|=-0,6a\ ( a< 0) \ \\ b) \ \sqrt{a^{4}( 3-a)^{2}} .\ a\geqslant 3\ \\ =a^{2} |3-a|\\ =a^{2}( a-3) =a^{3} -3a^{2} \ ( a\geqslant 3) \ \\ c) \ \sqrt{\frac{9+12a+4a^{2}}{b^{2}}} =\sqrt{\frac{( 2a+3)^{2}}{b^{2}}}\\ =\left| \frac{2a+3}{b}\right| =\frac{-2a-3}{b} \ ( vì\ a\geqslant -1,5\ và\ b< 0\ )\\ Bài\ 3:\ \\ a)\sqrt{16} x=8\ \\ \rightarrow 4x=8\ \\ \rightarrow x=2\ \\ b)\sqrt{9( x-1)} =21\ ( \ DK\ :x\geqslant 1)\\ \rightarrow 3\sqrt{x-1} =21\\ \rightarrow \sqrt{x-1} =7\\ \rightarrow x-1=49\\ \rightarrow x=50\ \\ c) \ \sqrt{4x^{2} +4x+1} =6\\ \rightarrow \sqrt{( 2x+1)^{2}} =6\\ \rightarrow |2x-1|=6\\ \rightarrow \begin{cases} 2x-1=6 & \\ 2x-1=-6 & \end{cases}\rightarrow \begin{cases} x=\frac{7}{2} & \\ x=\frac{-5}{2} & \end{cases}\\ \end{array}$
