Question

So sánh

a)\(4\sqrt{7}\) và \(3\sqrt{13}\)

b)\(\dfrac{1}{4}\sqrt{84}\) và \(6\sqrt{\dfrac{1}{7}}\)

Answer 1

a) Ta có: \(4\sqrt{7}=\sqrt{4^2.7}=\sqrt{112}\)

\(3\sqrt{13}=\sqrt{3^2.13}=\sqrt{117}\)

Vì 112 < 117 => \(\sqrt{112}< \sqrt{117}\) => \(4\sqrt{7}< 3\sqrt{13}\)

b) Ta có: \(\dfrac{1}{4}\sqrt{84}=\sqrt{\dfrac{21}{4}}=\sqrt{\dfrac{147}{28}}\)

\(6\sqrt{\dfrac{1}{7}}=\sqrt{\dfrac{36}{7}}=\sqrt{\dfrac{114}{28}}\)

Vì: \(\dfrac{147}{28}>\dfrac{114}{28}\Rightarrow\sqrt{\dfrac{147}{28}}>\sqrt{\dfrac{114}{28}}\Rightarrow\dfrac{1}{4}\sqrt{84}>6\sqrt{\dfrac{1}{7}}\)