Question

\(\sqrt{11}-\sqrt{3}và\sqrt{4}\)

so sánh

Answer 1

Ta có : \(\sqrt{16}-\sqrt{4}=4-2=2=\sqrt{4}\)

Mà \(\sqrt{16}>\sqrt{11};\sqrt{4}>\sqrt{3}\)

nên \(\sqrt{16}-\sqrt{4}>\sqrt{11}-\sqrt{3}\)

hay \(\sqrt{11}-\sqrt{3}< \sqrt{4}\)

Answer 2

Ta có : \(\sqrt{11}-\sqrt{3}=\left(\sqrt{11}-\sqrt{3}\right)^2=11-2\sqrt{33}+3=14-2\sqrt{33}\)

= \(14-\sqrt{132}\)

\(\sqrt{4}=\sqrt{16}-\sqrt{4}=\left(\sqrt{16}-\sqrt{4}\right)^2=16-2\sqrt{64}+4=20-\sqrt{256}\)

Dễ thấy : \(14< 20và132< 256\)

=> \(14-\sqrt{132}< 20-\sqrt{256}\)

hay : \(\sqrt{11}-\sqrt{3}< \sqrt{4}\)