Ta có :

a.  $\sqrt{1\frac{9}{16}.5\frac{4}{9}.0,01}=\sqrt{\frac{25}{16}.\frac{49}{9}.0,01}$

<=> $\sqrt{1\frac{9}{16}.5\frac{4}{9}.0,01}=\sqrt{\frac{25}{16}}.\sqrt{\frac{49}{9}}.\sqrt{0,01}$

<=> $\frac{5}{4}.\frac{7}{3}.0,1=\frac{3,5}{12}=\frac{7}{24}$

Vậy $\sqrt{1\frac{9}{16}.5\frac{4}{9}.0,01}=\frac{7}{24}$

b.   $\sqrt{1,44.1,21-1,44.0,4}=\sqrt{1,44.(1,21-0,4)}$

<=> $\sqrt{1,44.0,81}=\sqrt{1,44}.\sqrt{0,81}$

<=> $1,2.0,9=1,08$

Vậy  $\sqrt{1,44.1,21-1,44.0,4}=1,08$

c.  $\sqrt{\frac{165^{2}-124^{2}}{164}}=\sqrt{\frac{(165+124)(165-124)}{164}}$

<=> $\sqrt{\frac{289.41}{164}}=\sqrt{\frac{289}{4}}=\frac{17}{2}$

Vậy  $\sqrt{\frac{165^{2}-124^{2}}{164}}=\frac{17}{2}$

d.  $\sqrt{\frac{149^{2}-76^{2}}{457^{2}-384^{2}}}=\sqrt{\frac{(149+76)(149-76)}{(457+384)(457-384)}}$

<=> $\sqrt{\frac{225.73}{841.73}}=\frac{\sqrt{225}}{\sqrt{841}}=\frac{15}{29}$

Vậy $\sqrt{\frac{149^{2}-76^{2}}{457^{2}-384^{2}}}=\frac{15}{29}$