Question Number 199103 by tri26112004 last updated on 28/Oct/23
Commented by mr W last updated on 28/Oct/23
$$\sqrt[{{x}}]{\mathrm{4}}={x} \\ $$$$\mathrm{4}^{\frac{\mathrm{1}}{{x}}} ={x} \\ $$$$\mathrm{2}^{\frac{\mathrm{2}}{{x}}} ={x} \\ $$$$\Rightarrow{x}=\mathrm{2} \\ $$
Commented by mr W last updated on 28/Oct/23
$${more}\:{interesting}\:{is}\:{to}\:{find} \\ $$$$\:\:\:\:\:\sqrt[{...}]{\mathrm{5}} \\ $$$$\:\:\:\:\:\:\:\:\:\sqrt{\mathrm{5}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\sqrt{\mathrm{5}}\:\:=\:? \\ $$
Answered by deleteduser1 last updated on 28/Oct/23
$$\sqrt[{\sqrt[{...\sqrt{\mathrm{4}}}]{\mathrm{4}}}]{\mathrm{4}}=\sqrt[{\sqrt{\mathrm{4}}}]{\mathrm{4}}=\sqrt{\mathrm{4}}=\mathrm{2} \\ $$