Question

so sánh

\(\sqrt{3\sqrt{3}}\)  và  \(\sqrt{3}+1\)

Answer 1

\(\sqrt{3\sqrt{3}}=\sqrt{3.\sqrt{\dfrac{432}{144}}}< \sqrt{3\sqrt{\dfrac{625}{144}}}=\sqrt{3.\dfrac{25}{12}}=\dfrac{5}{2}\)

\(\sqrt{3}+1=\sqrt{\dfrac{12}{4}}+1>\sqrt{\dfrac{9}{4}}+1=\dfrac{3}{2}+1=\dfrac{5}{2}\)

\(\Rightarrow\sqrt{3}+1>\sqrt{3\sqrt{3}}\)