\(\left(\sqrt{18}+\sqrt{19}\right)^2=37+2\sqrt{18}\sqrt{19}\)
\(9^2=81\)
Có: \(18< 22\Rightarrow\sqrt{18}< \sqrt{22}\) , \(19< 22\Rightarrow\sqrt{19}< \sqrt{22}\)
\(\Rightarrow\sqrt{18}\sqrt{19}< \sqrt{22}\sqrt{22}=22\)
\(\Leftrightarrow2\sqrt{18}\sqrt{19}< 2\cdot22=44\)
\(\Leftrightarrow37+2\sqrt{18}\sqrt{19}< 37+44=81\)
\(\Rightarrow\left(\sqrt{18}+\sqrt{19}\right)^2< 9^2\)
\(\Rightarrow\sqrt{18}+\sqrt{19}< 9\)
ta có : \(\left(\sqrt{18}+\sqrt{19}\right)^2=\left(\sqrt{18}\right)^2+2\sqrt{18.19}+\left(\sqrt{19}\right)^2\)
\(=18+\sqrt{1368}+19=37+\sqrt{1368}\)
ta có : \(9^2=81=37+44=37+\sqrt{1936}\)
vì \(1936>1368\Rightarrow37+\sqrt{1368}< 37+\sqrt{1936}\)
\(\Rightarrow\sqrt{18}+\sqrt{19}< 9\)
