So sánh \(\sqrt {2015} + \sqrt {2018} \)và \(\sqrt {2016} + \sqrt {2017} \).

Xét: \({\left( {\sqrt {2015} + \sqrt {2018} } \right)^2} = 2015 + 2018 + 2\sqrt {2015.2018} = 4033 + 2\sqrt {2015.2018} \)

\({\left( {\sqrt {2016} + \sqrt {2017} } \right)^2} = 2016 + 2017 + 2\sqrt {2016.2017} = 4033 + 2\sqrt {2016.2017} \)

Ta so sánh: \(2\sqrt {2015.2018} \)và \(2\sqrt {2016.2017} \)thấy:

2015 . 2018 = 2015² + 3.2015

2016 . 2017 = 2015² + 3.2015 + 2

Suy ra: \(2\sqrt {2015.2018} \) < \(2\sqrt {2016.2017} \)

Vậy \(\sqrt {2015} + \sqrt {2018} \)< \(\sqrt {2016} + \sqrt {2017} \).