Question

sắp xếp theo thứ tự giảm dần
a.\(7\sqrt{2}\);\(2\sqrt{8}\);\(\sqrt{28}\)và \(5\sqrt{2}\)
b.\(3\sqrt{10}\);\(5\sqrt{3}\);\(\dfrac{20}{\sqrt{ }5}\)và 12\(\sqrt{\dfrac{2}{3}}\)

Answer 1

a)

\(7\sqrt{2}=\sqrt{49.2}=\sqrt{98}\\ 2\sqrt{8}=\sqrt{4.8}=\sqrt{32}\\ 5\sqrt{2}=\sqrt{25.2}=\sqrt{50}\)

Do 98 > 50 > 32 > 28 nên \(\sqrt{98}>\sqrt{50}>\sqrt{32}>\sqrt{28}\)

=> \(7\sqrt{2}>5\sqrt{2}>2\sqrt{8}>\sqrt{28}\)

b)

\(3\sqrt{10}=\sqrt{9.10}=\sqrt{90}\\ 5\sqrt{3}=\sqrt{25.3}=\sqrt{75}\)

\(\dfrac{20}{\sqrt{5}}=\dfrac{20\sqrt{5}}{5}=4\sqrt{5}=\sqrt{16.5}=\sqrt{80}\)

\(12\sqrt{\dfrac{2}{3}}=\sqrt{144.\dfrac{2}{3}}=\sqrt{96}\)

Do 96 > 90 > 80 > 75 => \(\sqrt{96}>\sqrt{90}>\sqrt{80}>\sqrt{75}\)

=> \(12\sqrt{\dfrac{2}{3}}>3\sqrt{10}>\dfrac{20}{\sqrt{5}}>5\sqrt{3}\)