Question Number 174755 by mnjuly1970 last updated on 10/Aug/22
Commented by kaivan.ahmadi last updated on 11/Aug/22
$${I}\subseteq\sqrt{{I}},{J}\subseteq\sqrt{{J}}\Rightarrow{I}+{J}\subseteq\sqrt{{I}}+\sqrt{{J}} \\ $$$$\Rightarrow\sqrt{{I}+{J}}\subseteq\sqrt{\sqrt{{I}}+\sqrt{{J}}} \\ $$$${on}\:{the}\:{other}\:{hand} \\ $$$$\sqrt{{I}}+\sqrt{{J}}\subseteq\sqrt{{I}+{J}}\Rightarrow\sqrt{\sqrt{{I}}+\sqrt{{J}}}\subseteq \\ $$$$\sqrt{\sqrt{{I}+{J}}}=\sqrt{{I}+{J}} \\ $$$$\blacksquare \\ $$$$ \\ $$$$ \\ $$