Question

So sánh :

a, \(\sqrt{3\sqrt{2}}\) và \(\sqrt{2\sqrt{3}}\)

b,\(\sqrt{10}+\sqrt{17}+1\) và \(\sqrt{61}\)

Answer 1

a , \(\sqrt{3\sqrt{2}}>\sqrt{2\sqrt{3}}\)

Answer 2

a,Ta có:\(\sqrt{3\sqrt{2}}=\sqrt{\sqrt{18}}\)
\(\sqrt{2\sqrt{3}}=\sqrt{\sqrt{12}}\)
Vì 12<18\(\Rightarrow\sqrt{12}< \sqrt{18}\)
\(\Rightarrow\sqrt{\sqrt{12}}< \sqrt{\sqrt{18}}\) hay \(\sqrt{2\sqrt{3}}< \sqrt{3\sqrt{2}}\)
b,Vì \(\sqrt{10}+\sqrt{17}+1>\sqrt{9}+\sqrt{16}+1\)
\(\Rightarrow\sqrt{10}+\sqrt{17}+1>3+4+1 \)
\(\Rightarrow\sqrt{10}+\sqrt{17}+1>8\)
\(\Rightarrow\sqrt{10}+\sqrt{17}+1>\sqrt{64}\)
Mà \(\sqrt{64}>\sqrt{61}\)
\(\Rightarrow\sqrt{10}+\sqrt{17}+1>\sqrt{61}\)