ta có \(\left(\sqrt{5\sqrt{3}}\right)^4=75\)
\(\left(\sqrt{3\sqrt{5}}\right)^4=45\)
\(\Rightarrow\sqrt{5\sqrt{3}}>\sqrt{3\sqrt{5}}\left(75>45\right)\)
Mình thấy cả 2 con trên đều bằng nhau .
\(\sqrt{5\sqrt{3}}\)và \(\sqrt{3\sqrt{5}}\)
\(\sqrt{5\sqrt{3}}\)= 2,94283................
\(\sqrt{3\sqrt{5}}\)= 2,59002...............
Ta thấy 2,94283......... > 2,59002.........Suy ra \(\sqrt{5\sqrt{3}}\) > \(\sqrt{3\sqrt{5}}\)
\(\sqrt{5\sqrt{3}}=\sqrt{\sqrt{5^2.3}}\)\(=\sqrt{\sqrt{75}}\)
\(\sqrt{3\sqrt{5}}=\sqrt{\sqrt{3^2.5}}\)\(=\sqrt{\sqrt{45}}\)
nhận thấy 75>45 => \(\sqrt{\sqrt{75}}>\sqrt{\sqrt{45}}\)
=>\(\sqrt{5\sqrt{3}}>\sqrt{3\sqrt{5}}\)
