So sánh: \(\sqrt{11}-\sqrt{3}\&2\)
\(\sqrt{11}=3,3166...\)
\(\sqrt{3}=1,7320...\)
\(\Rightarrow\sqrt{11}-\sqrt{3}=3,3166-1,7320=1,5846\)
\(1,5846< 2\Rightarrow\sqrt{11}-\sqrt{3}< 2\)
\(\sqrt{11}-\sqrt{3}\)và 2
\(\left(\sqrt{11}-\sqrt{3}\right)^2\)và 22=4
Ta có:\(\left(\sqrt{11}-\sqrt{3}\right)^2=14-2\sqrt{33}\)
\(4=14-10=14-2.5=14-2\sqrt{25}\)
Vì \(2\sqrt{25}< 2\sqrt{33}\)
\(\Rightarrow14-2\sqrt{33}< 14-2\sqrt{25}\). Hay \(\sqrt{11}-\sqrt{3}\)<2
