Question

So sánh\(\sqrt{11}\) - \(\sqrt{3}\) và 2

Answer 1

Có: \(\sqrt{16}-\sqrt{4}=4-2=2\)

mà \(\sqrt{16}>\sqrt{11};\sqrt{4}>\sqrt{3}\) nên \(\sqrt{16}-\sqrt{4}>\sqrt{11}-\sqrt{3}hay\sqrt{11}-\sqrt{3}< 2\)

Answer 2

ta có :

\(\left(\sqrt{11}-\sqrt{3}\right)^2=8-2\sqrt{33}\)

\(2^2=4\)

Do \(4>8-2\sqrt{33}\)

\(\Rightarrow2>\sqrt{11}-\sqrt{3}\)