So sánh
1) \(\sqrt{3\sqrt{2}}\) và \(\sqrt{2\sqrt{3}}\)
2) \(\sqrt{10}\)\(+\) \(\sqrt{17}\)\(+\)\(1\) và \(\sqrt{61}\)
3)\(\sqrt{31}\)\(-\)\(\sqrt{19}\)và \(\sqrt{2\sqrt{3}}\)
4) \(6\)\(-\)\(\sqrt{17}\)và \(\sqrt{61}\)
5)\(\sqrt{3+\sqrt{5}}\)và \(\frac{\sqrt{5}+1}{\sqrt{2}}\)
6)\(\sqrt{13}-\sqrt{12}\)và \(\sqrt{12}-\sqrt{11}\)
7)\(\sqrt{7+\sqrt{21}+4\sqrt{5}}\)và \(\sqrt{5}-1\)
\(1)\) Ta có :
\(\left(\sqrt{3\sqrt{2}}\right)^4=\left[\left(\sqrt{3\sqrt{2}}\right)^2\right]^2=\left(3\sqrt{2}\right)^2=9.2=18\)
\(\left(\sqrt{2\sqrt{3}}\right)^4=\left[\left(\sqrt{2\sqrt{3}}\right)^2\right]^2=\left(2\sqrt{3}\right)^2=4.3=12\)
Vì \(18>12\) nên \(\left(\sqrt{3\sqrt{2}}\right)^4>\left(\sqrt{2\sqrt{3}}\right)^4\)
\(\Rightarrow\)\(\sqrt{3\sqrt{2}}>\sqrt{2\sqrt{3}}\)
Vậy \(\sqrt{3\sqrt{2}}>\sqrt{2\sqrt{3}}\)
Chúc bạn học tốt ~
