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Bài 32. Tính
a) \( \sqrt{1\frac{9}{16}.5\frac{4}{9}.0,01}\);
b) \( \sqrt{1,44.1,21-1,44.0,4}\);
c) \( \sqrt{\frac{165^{2}-124^{2}}{164}}\);
d) \( \sqrt{\frac{149^{2}-76^{2}}{457^{2}-384^{2}}}\).
Hướng dẫn giải:
a)
\(\sqrt{1\frac{9}{16}.5\frac{4}{9}.0,01}=\sqrt{\frac{25}{16}.\frac{49}{9}}.\sqrt{0,01}\)
\(=\frac{5}{4}.\frac{7}{3}.0,1=\frac{3,5}{12}=\frac{7}{24}\)
b)
\(\sqrt{1,44.1,21-1,44.0,4}\)
\(=\sqrt{1,44(1,21-0,4)}\)
\(=\sqrt{1,44.0,81}\)
\(=\sqrt{1,44}.\sqrt{0,81}\)
\(=1,2.0,9=1,08\)
c)
\(\sqrt{\frac{165^{2}-124^{2}}{164}}\)
\(=\sqrt{\frac{(165-124)(165+124)}{164}}\)
\(=\sqrt{\frac{41.289}{41.4}}\)
\(=\sqrt{\frac{289}{4}}=\frac{17}{2}\)
Câu d:
\(\sqrt{\frac{149^{2}-76^{2}}{457^{2}-384^{2}}}\)
\(=\sqrt{\frac{(149-76)(149+76)}{(457-384)(457+384)}}\)
\(=\sqrt{\frac{73.225}{73.841}}\)
\(=\sqrt{\frac{225}{841}}=\frac{15}{29}\)