Question

So sánh

1) √0,5 và √(3) -2

2) √(2015) +√(2018) và √(2016) +√(2017)

Answer 1

Bài 2 :

Ta có : \(4066270< 4066272\)

=> \(2015.2018< 2016.2017\)

=> \(2\sqrt{2015.2018}< 2\sqrt{2016.2017}\)

=> \(2015+2\sqrt{2015.2018}+2018< 2016+2\sqrt{2016.2017}+2017\)

=> \(\left(\sqrt{2015}+\sqrt{2018}\right)^2< \left(\sqrt{2016}+\sqrt{2017}\right)^2\)

=> \(\sqrt{2015}+\sqrt{2018}< \sqrt{2016}+\sqrt{2017}\)

Câu 1 :

Ta thấy : 3 < 4

=> \(\sqrt{3}< \sqrt{4}=2\)

=> \(\sqrt{3}-2< 0\)

Mà \(\sqrt{0,5}>0\)

=> \(\sqrt{0,5}>\sqrt{3}-2\)