Question

So sánh : \(\sqrt{\sqrt{6}+\sqrt{20}}\) và \(\sqrt{1+\sqrt{5}}\)

Answer 1

https://i.imgur.com/sleTMHw.gif

Answer 2

\(\left\{{}\begin{matrix}\sqrt{6}>1\\\sqrt{20}\sqrt{5}\end{matrix}\right.\Rightarrow\sqrt{6}+\sqrt{20}>1+\sqrt{5}\Rightarrow\sqrt{\sqrt{6}+\sqrt{20}}>\sqrt{1+\sqrt{5}}\)

Answer 3

Lời giải:

Ta thấy: \(\sqrt{6}+\sqrt{20}=\sqrt{4}(\sqrt{1,5}+\sqrt{5})>\sqrt{1,5}+\sqrt{5}>1+\sqrt{5}\)

\(\Rightarrow \sqrt{\sqrt{6}+\sqrt{20}}>\sqrt{1+\sqrt{5}}\)