a)có\(\sqrt{12}=\sqrt{4\cdot3}=2\sqrt{3}\) VÌ\(3\sqrt{3}>2\sqrt{3}\)\(\Rightarrow3\sqrt{3}>\sqrt{12}\) b)có\(7=\sqrt{7^2}=\sqrt{49}\) \(3\sqrt{5}=\sqrt{3^2\cdot5}=\sqrt{45}\) Vì\(\sqrt{49}>\sqrt{45}\) \(\Rightarrow7>3\sqrt{5}\) c) có\(\sqrt{\left(\dfrac{1}{3}\right)^2\cdot51}=\sqrt{\dfrac{17}{3}}\) \(\dfrac{1}{5}\cdot\sqrt{150}=\sqrt{\left(\dfrac{1}{5}\right)^2\cdot150}=\sqrt{6}=\sqrt{\dfrac{18}{3}}\) Vì\(\sqrt{\dfrac{17}{3}}< \sqrt{\dfrac{18}{3}}\) \(\Rightarrow\dfrac{1}{3}\sqrt{51}>\dfrac{1}{5}\sqrt{150}\) d) có\(\dfrac{1}{2}\cdot\sqrt{6}=\sqrt{\left(\dfrac{1}{2}\right)^2\cdot6}=\sqrt{\dfrac{3}{2}}=\sqrt{1,5}\) \(6\sqrt{\dfrac{1}{2}}=\sqrt{6^2\cdot\dfrac{1}{2}}=\sqrt{18}\) Vì\(\sqrt{1,5}< \sqrt{18}\) \(\Rightarrow\dfrac{1}{2}\sqrt{6}< 6\sqrt{\dfrac{1}{2}}\) |
