a) Ta có:
\(\left\{ \matrix{ {\left( 5 \right)^3} = 125 \hfill \cr {\left( {\root 3 \of {123} } \right)^3} = 123 \hfill \cr} \right.\)
Vì \(125 > 123 \Leftrightarrow \root 3 \of {125} > \root 3 \of {123} \)
\( \Leftrightarrow5 > \root 3 \of {123}\)
Vậy \(5 > \root 3 \of {123} \).
b) Ta có:
\(\left\{ \matrix{ {\left( {5\root 3 \of 6 } \right)^3} = {5^3}.{\left( {\root 3 \of 6 } \right)^3} = 125.6 = 750 \hfill \cr {\left( {6\root 3 \of 5 } \right)^3} = {6^3}.{\left( {\root 3 \of 5 } \right)^3} = 216.5 = 1080 \hfill \cr} \right.\)
Vì \(750 < 1080 \Leftrightarrow \root 3 \of {750} < \root 3 \of {1080} \)
\(\Leftrightarrow 5\root 3 \of 6 < 6\root 3 \of 5\).
Vậy \(5\root 3 \of 6 < 6\root 3 \of 5\).
