Question

Which is greater of the two:

$\sqrt[3]{36}and\sqrt[5]{58}$

Answer 1

L.C.M. of 3 and 5 is 15
$\sqrt[3]{36}=\sqrt[3\times 5]{3\times 56^5}=\sqrt[15]{157776}$
$\sqrt[5]{58}=\sqrt[3\times 5]{3\times 58^3}=\sqrt[15]{15512}$
$\therefore$ $\sqrt[15]{157776}>\sqrt[15]{15512}\Rightarrow \sqrt[3]{36}>\sqrt[5]{58}$