Which one is bigger $\sqrt[1023]{1024}$ or $\sqrt[1024]{1023}$ Which one is bigger $\sqrt[1023]{1024}$ or $\sqrt[1024]{1023}$
I am really stuck with this one.My friend says that it can be solved by $AM-GM$
but I didn't succes.Any hints?

Raise both numbers to the power of $1023\cdot 1024$ to get $1024^{1024}$ and $1023^{1023}$. Which one looks bigger now?
Alternatively, pick your fravourite from among the two numbers $\sqrt[1023]{1023}$ or $\sqrt[1024]{1024}$, and compare each of the original two numbers to the one you picked.
