Question

Demonstrati ca \sqrt{2} > \sqrt[4]{3}

Answer 1

$\it \sqrt2\ \textgreater \ \sqrt[4]3 \Leftrightarrow (\sqrt2)^4\ \textgreater \ (\sqrt[4]3)^4 \Leftrightarrow 4\ \textgreater \ 3 \ (A)$

Answer 2

[tex] \sqrt2 $ $\boxed{?}$ $\sqrt[\big4]{3}\Big|^4 \ \\ (\sqrt2)^4$ $\boxed{?}$ $ (\sqrt[\big4]{3})^4\\ \\{\big(\sqrt2^2\big)}^2$ $ \boxed{?}$ $ 3 \\ \\ 2^2 $ $ \boxed{?} $ $ 3 \\ \\ 4 $ $\boxed{\ \textgreater \ }$ $ 3 \\ \\ \Rightarrow \boxed{\sqrt{2} \ \textgreater \ \sqrt[\big4]{3}}[/tex]