$a)\sqrt{1\dfrac{9}{16}.5\dfrac{4}{9}.0,01}=\sqrt{\dfrac{25}{16}.\dfrac{49}{9}.\dfrac{1}{100}}=\sqrt{\dfrac{25}{16}}.\sqrt{\dfrac{49}{9}}.\sqrt{\dfrac{1}{100}}=\dfrac{\sqrt{25}}{\sqrt{16}}.\dfrac{\sqrt{49}}{\sqrt{9}}.\dfrac{\sqrt{1}}{\sqrt{100}}=\dfrac{5}{4}.\dfrac{7}{3}.\dfrac{1}{10}=\dfrac{7}{24}
\\b)\sqrt{1,44.1,21-1,44-0,4}=\sqrt{1,44(1,21-0,4)}=\sqrt{1,44.0,81}=\sqrt{1,44}.\sqrt{0,81}=1,2.0,9=1,08
\\c)\sqrt{\dfrac{165^2-124^2}{164}}=\sqrt{\dfrac{(165+124)(165-124)}{164}}=\sqrt{\dfrac{289.41}{4.41}}=\sqrt{\dfrac{289}{4}}=\dfrac{\sqrt{289}}{\sqrt{4}}=\dfrac{17}{2}
\\d)\sqrt{\dfrac{149^2-76^2}{457^2-384^2}}=\sqrt{\dfrac{(149+76)(149-76)}{(457+384)(457-384)}}=\sqrt{\dfrac{225.73}{841.73}}=\sqrt{\dfrac{225}{841}}=\dfrac{\sqrt{225}}{\sqrt{841}}=\dfrac{15}{29}$