Câu 32:

Tính:

a) \(\sqrt{1 \frac{9}{16} \cdot 5 \frac{4}{9} \cdot 0,01}\)

b) \(\sqrt{1,44 \cdot 1,21-1,44.0,4}\)

c) \(\sqrt{\frac{165^{2}-124^{2}}{164}}\)

d) \(\sqrt{\frac{149^{2}-76^{2}}{457^{2}-384^{2}}}\)

Lời giải:

a) \(\sqrt{1 \frac{9}{16} \cdot 5 \frac{4}{9} \cdot 0,01}=\sqrt{\frac{25}{16} \cdot \frac{49}{9} \cdot \frac{1}{100}}\)

\(=\sqrt{\frac{25}{16}} \cdot \sqrt{\frac{49}{9}} \cdot \sqrt{\frac{1}{100}}\)

\(=\frac{5.7}{4.3 .10}=\frac{7}{24}\)

b) \(\sqrt{1,44 \cdot 1,21-1,44 \cdot 0,4}=\sqrt{1,44(1,21-0,4)}\)

\(=\sqrt{1,44 \cdot 0,81}\) \(=\sqrt{\frac{144}{100} \cdot \frac{81}{100}}=\frac{\sqrt{144}}{\sqrt{100}} \cdot \frac{\sqrt{81}}{\sqrt{100}}\)

\(=\frac{12}{10} \cdot \frac{9}{10}=\frac{108}{100}=1,08\)

c) \(\sqrt{\frac{165^{2}-124^{2}}{164}}=\sqrt{\frac{(165-124)(165+124)}{164}}=\sqrt{\frac{41.289}{164}}=\sqrt{\frac{289}{4}}=\frac{\sqrt{289}}{\sqrt{4}}=\sqrt{\frac{17^{2}}{2^{2}}}=\frac{17}{2}\)

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

\(=\sqrt{\frac{73.255}{73.841}}=\sqrt{\frac{255}{841}}\)

\(=\frac{\sqrt{255}}{\sqrt{841}}=\frac{\sqrt{15^{2}}}{\sqrt{29^{2}}}=\frac{15}{29}\)