a) Ta có:
\(\sqrt{1\dfrac{9}{16}.5\dfrac{4}{9}.0,01}=\sqrt{\dfrac{1.16+9}{16}.\dfrac{5.9+4}{9}.\dfrac{1}{100}}\)
\(=\sqrt{\dfrac{16+9}{16}.\dfrac{45+4}{9}.\dfrac{1}{100}}\)
\(=\sqrt{\dfrac{25}{16}.\dfrac{49}{9}.\dfrac{1}{100}}\)
\(=\sqrt{\dfrac{25}{16}}.\sqrt{\dfrac{49}{9}}.\sqrt{\dfrac{1}{100}}\)
\(=\dfrac{\sqrt{25}}{\sqrt{16}}.\dfrac{\sqrt{49}}{\sqrt{9}}.\dfrac{\sqrt{1}}{\sqrt{100}}\)
\(=\dfrac{\sqrt{5^2}}{\sqrt{4^2}}.\dfrac{\sqrt{7^2}}{\sqrt{3^2}}.\dfrac{1}{\sqrt{10^2}}\)
\(=\dfrac{5}{4}.\dfrac{7}{3}.\dfrac{1}{10}=\dfrac{5.7.1}{4.3.10}=\dfrac{35}{120}=\dfrac{7}{24}.\)
b) Ta có:
\(\sqrt{1,44.1,21-1,44.0,4} = \sqrt{1,44(1,21-0,4)}\)
\(=\sqrt{1,44.0,81}\)
\(=\sqrt{1,44}.\sqrt{0,81}\)
\(=\sqrt{1,2^2}.\sqrt{0,9^2}\)
\(=1,2.0,9=1,08\).
c) Ta có:
\(\sqrt{\dfrac{165^{2}-124^{2}}{164}}\)\(=\sqrt{\dfrac{(165-124)(165+124)}{164}}\)
\(=\sqrt{\dfrac{41.289}{41.4}}\) \(=\sqrt{\dfrac{289}{4}}\)
\(=\dfrac{\sqrt{289}}{\sqrt{4}}\) \(=\dfrac{\sqrt{17^2}}{\sqrt{2^2}}\) \(=\dfrac{17}{2}\).
d) Ta có:
\(\sqrt{\dfrac{149^{2}-76^{2}}{457^{2}-384^{2}}}\) \(=\sqrt{\dfrac{(149-76)(149+76)}{(457-384)(457+384)}}\)
\(=\sqrt{\dfrac{73.225}{73.841}}\) \(=\sqrt{\dfrac{225}{841}}\)
\(=\sqrt {\dfrac{15^2}{29^2}}=\dfrac{15}{29}\).
